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Abstract: This paper deals with the uniqueness of positive radial solutions to Dirichlet problems on annular domains in , . As an application we can obtain the results to equation , where , , and . [Copyright &y& Elsevier]

Abstract: In [C. Amrouche, V. Girault, J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator. An approach in weighted Sobolev spaces, J. Math. Pures Appl. 76 (1997) 55–81], authors study Dirichlet and Neumann problems for the Laplace operator in exterior domains of . This paper extends this study to the resolution of a mixed exterior Laplace''s problem. Here, we give existence, unicity and regularity results in ''s theory with , in weighted Sobolev spaces. [Copyright &y& Elsevier]

Abstract: We examine properties of eigenvalues and solutions to a 2n-dimensional Stieltjes Sturm–Liouville eigenvalue problem. Existence and uniqueness of a solution has been established previously. An earlier paper considered the corresponding initial value problem and established conditions which guarantee that solutions depend continuously on the coefficients [L.E. Battle, Solution dependence on problem parameters for initial value problems associated with the Stieltjes Sturm–Liouville equations, Electron. J. Differential Equations 2005 (2) (2005) 1–18]. Here, we find conditions which guarantee that the eigenvalues and solutions depend continuously on the coefficients, endpoints, and boundary data. For a simplified two-dimensional problem, we find conditions which guarantee the eigenvalues to be differentiable functions of the problem data. [Copyright &y& Elsevier]

Abstract: This paper examines the time-dependent double diffusive convection in Brinkman flow in a semi-infinite cylinder. Under appropriate initial and boundary conditions the authors establish exponential decay of solutions in “energy” norm with distance from the finite end of the cylinder. [Copyright &y& Elsevier]

Abstract: This paper presents a partial classification for type-changing symplectic Monge–Ampère partial differential equations (PDEs) that possess an infinite set of first-order intermediate PDEs. The normal forms will be quasi-linear evolution equations whose types change from hyperbolic to either parabolic or to zero. The zero points can be viewed as analogous to singular points in ordinary differential equations. In some cases, intermediate PDEs can be used to establish existence of solutions for ill-posed initial value problems. [Copyright &y& Elsevier]

Abstract: This paper deals with the solvability and uniqueness of the second-order three-point boundary value problems at resonance on a half-line and where , are continuous and . By using the coincidence degree theory, we establish some existence and uniqueness criteria. [Copyright &y& Elsevier]

Abstract: In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of . [Copyright &y& Elsevier]

Abstract: In this paper we provide a formulation of initial value problems for (explicit and implicit) difference equations in terms of abstract equations in sequence spaces. They will be solved using appropriate fixed point theorems and we obtain quantitative attractivity properties. [Copyright &y& Elsevier]

Abstract: In this paper, the competitor–competitor–mutualist three-species Lotka–Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction–diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the spectral theory for the second-order left definite difference boundary value problems. Existence of eigenvalues of boundary value problems is proved, numbers of their eigenvalues are calculated and fundamental spectral results are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the limit behaviour of optimal control problems governed by elliptic boundary value problems with equivalued surface when the equivalued surface boundary shrinks to a fixed point on the outer boundary of a bounded domain. [Copyright &y& Elsevier]

Abstract: This paper deals with the second order three-point boundary value problem The existence and multiplicity of positive solutions are investigated by means of the fixed point theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper, we provide sufficient conditions for the existence of at least three solutions to a three-point boundary value problem for higher-order ordinary differential equations. The nonlinear term f in the differential equation under consideration may depend on higher-order derivatives of arbitrary order and this is where the main novelty of this work lies. By applying the two pairs of upper and lower solutions method of Henderson and Thompson, as well as degree theory, the existence of at least three solutions of the problem is given. [Copyright &y& Elsevier]

Abstract: In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation where and H is the Heaviside function, with boundary condition , where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution. [Copyright &y& Elsevier]

Abstract: This paper is concerned with boundary value problems for systems of nonlinear second-order differential equations. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems. [Copyright &y& Elsevier]

Abstract: Let be a bounded time-scale, with , . We consider the weighted, linear, eigenvalue problem for suitable functions p, q and w and . Problems of this type on time-scales have normally been considered in a setting involving Banach spaces of continuous functions on . In this paper we formulate the problem in Sobolev-type spaces of functions with generalized -type derivatives. This approach allows us to use the functional analytic theory of Hilbert spaces rather than Banach spaces. Moreover, it allows us to use more general coefficient functions p, q, and weight function w, than usual, viz., and compared with the usual hypotheses that , . Further to these conditions, we assume that on , on , for some constants . These conditions are similar to the usual assumptions imposed on Sturm–Liouville, ordinary differential equation problems. We obtain a min–max characterization of the eigenvalues of the above problem, and various eigenfunction expansions for functions in suitable function spaces. These results extend certain aspects of the standard theory of self-adjoint operators with compact resolvent to the above problem, even though the linear operator associated with the left-hand side of the problem is not in fact self-adjoint on general time-scales. [Copyright &y& Elsevier]

Abstract: In this paper, a food chain model with ratio-dependent functional response is studied under homogeneous Neumann boundary conditions. The large time behavior of all non-negative equilibria in the time-dependent system is investigated, i.e., conditions for the stability at equilibria are found. Moreover, non-constant positive steady-states are studied in terms of diffusion effects, namely, Turing patterns arising from diffusion-driven instability (Turing instability) are demonstrated. The employed methods are comparison principle for parabolic problems and Leray–Schauder Theorem. [Copyright &y& Elsevier]

Abstract: In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations. [Copyright &y& Elsevier]

Abstract: In this paper, the dynamic analysis of 3-D composite beam elements restrained at their edges by the most general boundary conditions and subjected in arbitrarily distributed dynamic loading is presented. For the solution of the problem at hand, a boundary element method is developed for the construction of the 14×14 stiffness matrix and the nodal load vector of a member of an arbitrarily shaped composite cross section, taking into account both torsional warping and shear deformation effects, which together with the corresponding mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach. Both free and forced vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance. Numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy. [Copyright &y& Elsevier]

Abstract: In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales where is p-Laplacian operator, i.e., , . Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel''skii''s fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied. [Copyright &y& Elsevier]

Abstract: The present paper is devoted to the study of a boundary value problem for abstract first order linear differential equation with integral boundary conditions. We obtain necessary and sufficient conditions for the unique solvability and well-posedness. We also study the Fredholm solvability. Finally, we obtain a result of the stability of solution with respect to small perturbation. [Copyright &y& Elsevier]

Abstract: In this paper we show that, under suitable assumptions, the solutions to the approximating initial and boundary value problems (cf. introduction) converge in , for suitable indexes and , to the solution to the limit problem . The last two Sections 4–5 are devoted to a similar approximation result, in a Banach-space framework, and involve a generalization of the kernels k, h and operator A. [Copyright &y& Elsevier]

Abstract: Let ϕ and θ be two increasing homeomorphisms from onto with , . Let be a function satisfying Carathéodory''s conditions, and for each i, , let , be a continuous function, with , , . In this paper we first prove a suitable continuation lemma of Leray–Schauder type which we use to obtain several existence results for the m-point boundary value problem: We note that this problem is at resonance, in the sense that the associated m-point boundary value problem has the non-trivial solution , where is an arbitrary constant vector, in view of the assumption . [Copyright &y& Elsevier]

Abstract: In this paper we consider a fourth order linear ordinary differential operator in one space dimension. We impose, at each endpoint, one general Wentzell boundary condition as well as one other linear boundary. Our goal is to classify precisely when these operators are symmetric, semibounded and/or quasiaccretive. In particular these results extend the collection of boundary conditions for which the one-dimensional beam equation is well-posed. [Copyright &y& Elsevier]

Abstract: This paper deals with the critical exponents for the quasi-linear parabolic equations in and with an inhomogeneous source, or in exterior domains and with inhomogeneous boundary conditions. For , and , we obtain that is the critical exponent of these equations. Furthermore, we prove that if , then every positive solution of these equations blows up in finite time; whereas these equations admit the global positive solutions for some and some initial data if . Meantime, we also demonstrate that every positive solution of these equations blows up in finite time provided , and . [Copyright &y& Elsevier]

Abstract: In electrical impedance tomography, one tries to recover the conductivity inside a body from boundary measurements of current and voltage. In many practically important situations, the object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. It has been shown that the inhomogeneities can be characterized by the factorization technique if the conductivity coefficient jumps to a higher or lower value on the boundaries of the inclusions. In this paper, we extend the results to the case of weaker inclusions: If the inhomogeneities inside the body are more (or less) conductive than the known background, if the conductivity coefficient and its lowest normal derivatives are continuous over the inclusion boundaries, and if the mth normal derivative of the conductivity jumps on the inclusion boundaries, then the factorization method provides an explicit characterization of the inclusions. [Copyright &y& Elsevier]

Abstract: Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem Applications of our results to the special case where f is a power function of u and its derivatives are also discussed. Moreover, similar conclusions for a more general higher order boundary value problem are established. Our results extend some recent work in the literature on boundary value problems for ordinary differential equations. The analysis of this paper mainly relies on fixed point theorems on cones. [Copyright &y& Elsevier]

Abstract: The cubic nonlinear Schrödinger (NLS) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The “nonlinear” spectrum of the associated Lax pair reveals topological properties of the NLS phase space that are difficult to assess by other means. In this paper we use the invariance of the nonlinear spectrum to examine the long time behavior of exponential and multisymplectic integrators as compared with the most commonly used split step approach. The initial condition used is a perturbation of the unstable plane wave solution, which is difficult to numerically resolve. Our findings indicate that the exponential integrators from the viewpoint of efficiency and speed have an edge over split step, while a lower order multisymplectic is not as accurate and too slow to compete. [Copyright &y& Elsevier]

Abstract: The challenge of modeling low-speed rarefied gas flow in the transition regime is well known. In this paper, we propose a numerical solution procedure for the regularized 13 moment equations within a finite-volume framework. The stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first-order approximation. To model confined flows, a complete set of wall boundary conditions for the 13 moment equations are derived based on the Maxwell wall-boundary model. This has been achieved by expanding the molecular distribution function to fourth-order accuracy in Hermite polynomials. Empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation Monte Carlo data. The numerical predictions obtained from the regularized 13 moment equations and the Navier–Stokes–Fourier equations are compared with data generated using the direct simulation Monte Carlo method for planar Couette flow. For a range of wall velocities and Knudsen numbers (0.012–1.0), the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation Monte Carlo data. The results also highlight limitations that are caused by the use of a first-order expansion of the third moment. [Copyright &y& Elsevier]

Abstract: In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition , . So the Esquivel-Avila''s results are generalized and improved. [Copyright &y& Elsevier]

Abstract: Asymptotic stability by Lyapunov of the steady-state solution to the linear initial-boundary value problem which is formulated in the first part of this paper [A.M. Blokhin, D.L. Tkachev, L.O. Baldan, Well-posedness of a modified initial-boundary value problem on stability of shock waves in a viscous gas. Part I, J. Math. Anal. Appl. 331 (1) (2007) 408–423 (this issue)] proved under two conditions. The main of these conditions is that zeros of Lopatinsky determinant excluding , lie in the left half-plane. The problem arises while providing grounds for replacing of thin transitional zones of strong gradients of basic flow parameters for viscous heat-conducting gas with surfaces of strong discontinuity. [Copyright &y& Elsevier]

Abstract: This paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established. [Copyright &y& Elsevier]

Abstract: This paper deals with impulsive advanced ordinary differential equations with boundary conditions. We investigate the existence of solutions and quasisolutions for advanced impulsive differential equations. To obtain such results we apply Schauder''s fixed point theorem. Corresponding results are also formulated for differential inequalities. [Copyright &y& Elsevier]

Abstract: In this paper we study some asymptotic profiles of shape functions of self-similar solutions to the initial-boundary value problem with Neumann boundary condition for the generalized KPZ equation: , where q is positive number. The shapes of solutions of the corresponding nonlinear ordinary differential equation are of very different nature. The properties depend on the critical value and initial data as usual. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of positive solutions for the boundary value problem of one-dimensional p-Laplacian with delay. The proof is based on the Guo–Krasnoselskii fixed-point theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesús Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119–137; Debra L. Etheridge, Jesús Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127–144]. [Copyright &y& Elsevier]

Abstract: The Ginzburg–Landau equation has been used as a simplified mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study a generalized complex Ginzburg–Landau equation in two spatial dimension with a fifth order nonlinear term and cubic terms containing spatial derivatives. We prove a global existence and uniqueness theorem. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii''s fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem. [Copyright &y& Elsevier]

Abstract: This work is a continuation of our previous work [Z.-Q. Shao, D.-X. Kong, Y.-C. Li, Shock reflection for general quasilinear hyperbolic systems of conservation laws, Nonlinear Anal. TMA 66 (1) (2007) 93–124]. In this paper, we study the global structure instability of the Riemann solution containing shocks, at least one rarefaction wave for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the nonexistence of global piecewise solution to a class of the mixed initial-boundary value problem for general quasilinear hyperbolic systems of conservation laws on the quarter plane. Our result indicates that this kind of Riemann solution mentioned above for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable. Some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given. [Copyright &y& Elsevier]

Abstract: In this paper, the three-point boundary value problem and its conjugate boundary value problem are studied under some conditions concerning the same first eigenvalue of the both linear problems. By applying the fixed point index theory, the coexistence of single and multiple positive solutions of the above mentioned problems is verified. As an application, some examples are given to illustrate our results. [Copyright &y& Elsevier]

Abstract: In the present paper, a class of Dirichlet problem with discontinuous nonlinearities super-linear or asymptotically linear at infinity is studied, and some new existence theorems of solutions are obtained. [Copyright &y& Elsevier]

Abstract: In this paper, the second-order four-point boundary value problem is studied, where , , and , are nonnegative continuous functions. By the use of the property of the corresponding Green''s function, fixed-point index theory, Leray–Schauder degree and upper and lower solution method, some existence, nonexistence, and multiplicity results of positive solutions are acquired. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence and multiplicity of symmetric positive solutions for the following second-order three-point boundary value problem where is symmetric on and maybe singular at and , is continuous and is symmetric on for all . Growth conditions are imposed on f which yield the existence of at least one or at least two positive solutions. Our proof based on Krasnoselskii''s fixed point theorem in a cone. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence and multiplicity of positive periodic solutions for first-order vector differential equation , a.e. under the periodic boundary value condition . Here ω is a positive constant, and is a Carathéodory function. Some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the form where m is a given positive integer and is continuous. We introduce a new maximum principle of higher order equations and develop a monotone method in the presence of lower and upper solutions for this problem. [Copyright &y& Elsevier]

Abstract: In this paper we study nonlinear, discrete, multipoint boundary value problems of the form subject to We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter ϵ. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of positive solutions as well as positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity may be singular at , , and/or , . [Copyright &y& Elsevier]

Abstract: We investigate an initial-boundary value problem for equations of Benjamin–Bona–Mahony (BBM) type in two different physical situations. In the first, the mixed problem is considered on a cylinder domain Q of . In the second one, the mixed problem is studied inside of an increasing noncylindrical domain of . In both situations we show the existence of a unique nonlocal solution. In cylindrical case it is proved the existence of weak and strong solutions, regularity of strong solutions, and in noncylindrical case weak solutions. One of the goals of this paper is to show that the noncylindrical problem is well-posed by using the penalty method idealized by Lions [J.L. Lions, Une remarque sur les problèmes d''évolution non linéaires dans des domaines non cylindriques, Rev. Roumaine Math. Pures Appl. 9 (1964) 11–18]. [Copyright &y& Elsevier]

Abstract: In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions. [Copyright &y& Elsevier]

Abstract: In this paper we consider an initial boundary-value problem related to the electrodynamics of vibrating elastic media. The aim is to prove an existence and uniqueness result for a model describing the nonlinear interactions of the electromagnetic and elastic waves. We assume that the motion of the continuum occurs at velocities that are much smaller than the propagation velocity of the electromagnetic waves through the elastic medium. The model under study consists of two coupled differential equations, one of them is the hyperbolic equation (an analog of the Lamé system) and another one is the parabolic equation (an analog of the diffusion Maxwell system). One stability result is proved too. [Copyright &y& Elsevier]