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Abstract: In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation , , subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems. [Copyright &y& Elsevier]

Abstract: In this paper, the second-order m-point boundary value problem is studied, where , . We give at first the associated Green''s function and its properties for the m-point boundary value problem, and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of solutions for weighted -Laplacian ordinary system boundary value problems via Leray–Schauder degree, the sufficient conditions for the existence of solutions be given. As an application, we obtain the existence of the radial solutions for the -Laplacian partial differential system Dirichlet problems. [Copyright &y& Elsevier]

Abstract: In this paper, we present some general results of existence and uniqueness of solutions of nonlinear two-point boundary value problems for third-order nonlinear differential equations by using the Shooting method. As applications we give certain concrete sufficient conditions for the existence and uniqueness. [Copyright &y& Elsevier]

Abstract: Generalising the method presented in an earlier paper an analytical solution is presented for the natural frequencies, mode shapes and orthogonality conditions of an arbitrary system of Euler–Bernoulli beams interconnected by arbitrary joints and subject to arbitrary boundary conditions. [Copyright &y& Elsevier]

Abstract: In this paper, by algebraic method and Lyapunov function, we discuss the stability of non-hyperbolic equilibrium point in , that the coefficient matrix of linearized system have a pair purely imaginary eigenvalues and a zero eigenvalue, with the perturbations of 3th-degree homogeneous and 3th-degree and 5th-degree homogeneous. We shall give the sufficiently conditions which can immediately distinguish that the equilibrium point is asymptotically stable or unstable and a ball-center by the coefficients of perturbed terms, meantime, we discuss the condition which produce invariant closed surface by changing the stability of equilibrium point with perturbation. [Copyright &y& Elsevier]

Abstract: In this paper, the critical point theory is employed to establish existence and multiple solutions for a second-order difference boundary value problem. [Copyright &y& Elsevier]

Abstract: This paper presents a variety of existence results for nonlinear multi-point boundary value problem on the half-line. In particular, we consider Existence results are established using fixed-point theorems on cone. [Copyright &y& Elsevier]

Abstract: In this paper we prove an existence and uniqueness theorem for the Dirichlet problem for linear elliptic equations (in unbounded domains) whose leading coefficients are locally VMO and satisfy a suitable condition at infinity. [Copyright &y& Elsevier]

Abstract: This paper discusses nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type. The lower and upper solutions and monotone iterative techniques are used to achieve the existence results. Two examples are provided to illustrate the efficiency of the obtained results. [Copyright &y& Elsevier]

Abstract: In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a fourth-order nonlinear parabolic equation. [Copyright &y& Elsevier]

Abstract: In this paper, by using Schaeffer''s theorem, we prove new existence theorems for a nonlinear periodic boundary value problem of first-order differential equations with impulses. Our results improve and generalize some known results. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to obtain a high order full discretization of the initial value problem for the linear Schrödinger equation in a finite computational domain. For this we use a high order finite element discretization in space together with an adaptive implementation of local absorbing boundary conditions specifically obtained for linear finite elements, and a high order symplectic time integrator. The numerical results show that it is possible to obtain simultaneously a very good absorption at the boundary and a very small error in the interior of the computational domain. [Copyright &y& Elsevier]

Abstract: In this paper we consider the existence of positive solutions of the following boundary value problem: where are the increasing homeomorphism and positive homomorphism and , . We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion–expression fixed point theorem. [Copyright &y& Elsevier]

Abstract: We analyze the dynamics of a reaction–diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. [Copyright &y& Elsevier]

Abstract: This paper is devoted to regularity results and geometric properties of the singular set of the parabolic obstacle problem with variable right-hand side. Making use of a monotonicity formula for singular points, we prove the uniqueness of blow-up limits at singular points. These results apply to parabolic obstacle problem with variable coefficients. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence and multiplicity of positive solutions for the differential equations system where are parameters, , , and . The system is a semi-positone problem since the nonlinear term is allowed to take negative values and may change sign on . The results are established via fixed point index theory. [Copyright &y& Elsevier]

Abstract: In this paper, some sufficient conditions for the existence of solutions to the boundary value problems of a class of second order difference equation are obtained by using the critical point theory. [Copyright &y& Elsevier]

Abstract: In this paper, we consider an initial boundary value problem for some nonlinear evolution system with dissipation and ellipticity. We establish the global existence and furthermore obtain the () decay rates of solutions corresponding to diffusion waves. The analysis is based on the energy method and pointwise estimates. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the existence of solutions to systems of second order differential inclusions with maximal monotone terms. Our proofs rely on the theory of maximal monotone operators and the Schauder degree theory. A notion of solution-tube to these problems is introduced. This notion generalizes the notion of upper and lower solutions of second order differential equations. [Copyright &y& Elsevier]

Abstract: In this paper we study a semilinear heat equation in a long cylindrical region if the far end and the lateral surface are held at zero temperature and a nonzero temperature is applied at the near end. Our aim is to derive some explicit spatial decay bounds for the solution and its derivatives and to show that the solution depends continuously on the data at the near end of the cylinder. [Copyright &y& Elsevier]

Abstract: We proved recently that parabolic initial value problems with discontinuous nonlinearities have no unique weak solution in general, but have a unique generalized solution in the sense of Colombeau. In this paper we study the relationship between generalized solutions and weak solutions. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem where λ is a positive parameter. Under various assumptions on a and f we establish intervals of the parameter λ which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii''s fixed point theorem of cone expansion–compression type. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of positive solutions of the semilinear elliptic equation , with and . Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of positive solutions for fourth order singular m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in and construct lower and upper solutions to give a necessary and sufficient condition for the existence of as well as positive solutions. Our nonlinearity may be singular at x, y, and/or . [Copyright &y& Elsevier]

Abstract: This paper deals with the existence and uniqueness for the nth-order periodic boundary value problem where is an nth-order linear differential operator and is continuous. We present some spectral conditions for the nonlinearity to guarantee the existence and uniqueness. These spectral conditions are the generalization for nonresonance condition of Duffing equation. [Copyright &y& Elsevier]

Abstract: In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L 2 stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy. [Copyright &y& Elsevier]

Abstract: In this paper we consider nonlinear boundary value problems whose simplest model is the following: where is a summable function in Ω (bounded open set in , ), , and . [Copyright &y& Elsevier]

Abstract: In this paper we study the existence of positive solutions of a second-order integral boundary value problems for ordinary differential equations. Our results presented here unify, generalize and substantially improve the existing results in the literature. Moreover, it is worthwhile to point out that our method will dispense with constructing a new Green function. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of positive solutions to the fourth order boundary value problem where , , for are given constants satisfying some suitable conditions. The proofs are based on the fixed point index theorem in cones. [Copyright &y& Elsevier]

Abstract: In this paper we study the existence and multiplicity of nontrivial solutions for a boundary value problem associated with a semilinear sixth-order ordinary differential equation arising in the study of spatial patterns. Our treatment is based on variational tools, including two Brezis–Nirenberg''s linking theorems. [Copyright &y& Elsevier]

Abstract: A method to identify moving forces on a continuous bridge has been developed in this paper. The bridge is modelled as a Bernoulli–Euler beam and the boundary value problem of the beam is solved to get the exact mode shape functions of the vibrating beam with intermediate supports. As the number of spans of the bridge increases, the identification accuracy decreases and at the same time more execution time is needed to finish one case study. To minimize this problem, a method has been developed to identify moving forces on a selected span of interest from the continuous bridge. The Singular Value Decomposition (SVD) of the coefficient matrix of the overdetermined equation is used in the solution. To evaluate the method, simulations of two moving forces on a continuous bridge and on one selected span from the continuous bridge are studied. White noise is added to the simulated bending moment and acceleration responses to study the effect of noise in moving forces identification problem for different numbers and arrangements of sensors. The results obtained from the simulation study show that the method is effective in identifying moving forces and acceptable results can be obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones. [Copyright &y& Elsevier]

Abstract: In this paper, by using the cone theory and the monotone iterative technique, we investigate the existence of maximal and minimal solutions of the initial value problem for second order impulsive differential equations which nonlinearly involve the derivative in Banach space and give an example to illustrate our results. [Copyright &y& Elsevier]

Abstract: In this paper we study bifurcation from simple eigenvalues for systems of differential equations; we prove the existence of global bifurcating branches of solutions on which the Maslov index of suitable associated linear systems is preserved. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of Lyapunov-type inequalities () for linear partial differential equations. More precisely, we treat the case of Neumann boundary conditions on bounded and regular domains in . It is proved that the relation between the quantities p and plays a crucial role. This fact shows a deep difference with respect to the ordinary case. The linear study is combined with Schauder fixed point theorem to provide new conditions about the existence and uniqueness of solutions for resonant nonlinear problems. [Copyright &y& Elsevier]

Abstract: This paper proves that any initial condition in the energy space for the plate equation with square root damping on a smooth bounded domain, with hinged boundary conditions , can be steered to zero by a square integrable input function u supported in arbitrarily small time interval and subdomain. As T tends to zero, for initial states with unit energy norm, the norm of this u grows at most like for any real and some . Indeed, this fast controllability cost estimate is proved for more general linear elastic systems with structural damping and non-structural controls satisfying a spectral observability condition. Moreover, under some geometric optics condition on the subdomain allowing to apply the control transmutation method, this estimate is improved into and the dependence of on the subdomain is made explicit. These results are analogous to the optimal ones known for the heat flow. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the use of the Timoshenko beam model for free vibration analysis of multi-walled carbon nanotubes (CNTs). Unlike the Euler beam model, the Timoshenko beam model allows for the effects of transverse shear deformation and rotary inertia. These effects become significant for CNTs with small length-to-diameter ratios that are normally encountered in applications such as nanoprobes. By using the differential quadrature (DQ) method, the governing Timoshenko equations are solved for CNTs of different length-to-diameter ratios and boundary conditions. By comparing results based on the Timoshenko and the Euler beam theories, we show that the frequencies are significantly overpredicted by the Euler beam theory when the length-to-diameter ratios are small and when considering high vibration modes. For such situations, the Timoshenko beam model should be used for a better prediction of the frequencies. [Copyright &y& Elsevier]

Abstract: In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green''s formula is defined for piecewise differentiable functions. Properties of Green''s functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green''s function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation , , satisfying either the conjugate boundary conditions or the right focal boundary conditions , where a and f are positive. We show that there exists a such that the above boundary value problem has at least two, one and no positive solutions for , and , respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution of the problem depends continuously on the parameter λ, i.e., is nondecreasing in λ, and . [Copyright &y& Elsevier]

Abstract: We show in this paper that there exist domains Ω, which are not conformally equivalent to starshaped domains, such that the Dirichlet problem: , in Ω; on ∂Ω has no solution. Some nonexistence results about the Dirichlet problem: , in Ω; on ∂Ω for certain over three dimensional non-starshaped domains are also obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non-linearity and combine these results with the localization method introduced in [López-Gómez, The boundary blow-up rate of large solutions, J. Differential Equations 195 (2003) 25–45] to prove that any large solution of , , , must satisfywhereand is any smooth extension of the boundary normal section of a at , i.e.,Subsequently, stands for the outward unit normal at . Therefore, the theory can be extended to cover the general case when . [Copyright &y& Elsevier]

Abstract: A connection between the semigroup of the Cauchy process killed upon exiting a domain D and a mixed boundary value problem for the Laplacian in one dimension higher known as the mixed Steklov problem, was established in [R. Bañuelos, T. Kulczycki, The Cauchy process and the Steklov problem, J. Funct. Anal. 211 (2004) 355–423]. From this, a variational characterization for the eigenvalues , , of the Cauchy process in D was obtained. In this paper we obtain a variational characterization of the difference between and . We study bounded convex domains which are symmetric with respect to one of the coordinate axis and obtain lower bound estimates for where is the eigenvalue corresponding to the “first” antisymmetric eigenfunction for D. The proof is based on a variational characterization of and on a weighted Poincaré-type inequality. The Poincaré inequality is valid for all α symmetric stable processes, , and any other process obtained from Brownian motion by subordination. We also prove upper bound estimates for the spectral gap in bounded convex domains. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions. We show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary. The included application to a size structured population equation provides a motivation for abstract results. [Copyright &y& Elsevier]

Abstract: In this paper, we study a class of superlinear semipositone singular second order Dirichlet boundary value problem. A sufficient condition for the existence of positive solution is obtained under the more simple assumptions. [Copyright &y& Elsevier]

Abstract: In this paper, we study the asymptotic behaviour as of the radial solution of the problem where is an annulus of , . [Copyright &y& Elsevier]

Abstract: The aim of the paper is to prove optimal results on local and global uniform convergence of solutions to elliptic equations with Dirichlet boundary conditions on varying domains. We assume that the limit domain be stable in the sense of Keldyš [Amer. Math. Soc. Transl. 51 (1966) 1–73]. We further assume that the approaching domains satisfy a necessary condition in the inside of the limit domain, and only require -convergence outside. As a consequence, uniform and -convergence are the same in the trivial case of homogenisation of a perforated domain. We are also able to deal with certain cracking domains. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the exact number of positive solutions for boundary value problems and , where and is a positive parameter. We consider the case in which the nonlinearity f is positive on and changes sign from negative to positive. [Copyright &y& Elsevier]

Abstract: In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian subject to the boundary value conditions: where , , with , and satisfy , , and . Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. [Copyright &y& Elsevier]

Abstract: In this paper, a non-variational version of a max–min principle is extended, and some unique existence results for the periodic boundary value problem of the higher order nonconservative systems with resonance are obtained. [Copyright &y& Elsevier]