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This paper investigates the existence of weak solutions for a Dirichlet boundary value problem of p(x)-K.irchhoff type driven by p(x)-Laplacian-like operators, arising from the capillarity phenomena. The existence is proved by using the topological degree for a class of demicontinuous operators of generalized (S+) type and the theory of variable-exponent Sobolev spaces. Our result extends some recent work in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove two existence results for impulsive differential equations with fixed double parameters. Our main tool is based on variational methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for semilinear fractional differential inclusion multi-term problem in a more general form. A fixed point strategy is used to establish existence of solutions, namely Leray-Schauder fixed point alternative for set-valued maps. Two cases are considered convexity and non convexity of set-valued function. Illustrative examples are provided at the end of our theorems to ensure the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and stability of the solution for a non-linear fractional boundary value problem. The existence is shown by Leray-Schauder's non-linear alternative under a special working space. Also, the Ulam-Hyers stability of solution is analyzed. To illustrate our findings, an example is presented. [ABSTRACT FROM AUTHOR]

Thi.s paper ix concerned with the existence of solutions for deformable fractional differential inclusion [(DF (DI] with boundary conditions iii Banach spaces. In the set-valued (multivalued) function. the investigation is reliable for both convex and non-convex values. In addition, we illustrate our results via applications of our abstract theory. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence and uniqueness results for approximate solution for a couple of nonlinear periodic boundary value problems of first order nonlinear functional delay differential equations via construction of the algorithms for solutions. The main results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorems of Dhage (2014) in a partially ordered complete normed linear space. Examples are also furnished to illustrate the hypotheses and the abstract results of this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive solutions for a sequence of caputo fractional differential equation. By the application of Guo-Krasnoselskii Theorem, we prove the existence of at least one positive solution. To prove the uniqueness of solution we use Banach contraction principle. Two examples are given to verify the obtained results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to show the existence and comparison of smallest eigenvalues of (n. p)-type Riemann-Liouville fractional boundary value problems. The techniques involve the theory of /4,-positive operators on a Banach space. We emphasize that the Banach space used in this work appears to be distinct from the space used when tackling boundary value problems for ordinary differential equations. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate a boundary value problem for fractional differential equation with integral and fractional integro-differential conditions. Some new existence results are obtained using Mönch fixed point theorems and measure of noncompactness. Our theoretical results are supported by some illustrative examples. [ABSTRACT FROM AUTHOR]

This paper deals with some existence. uniqueness and k-Mittag-Leffier-Ulam-Hyers stability results for a class of boundary value problem for implicit nonlinear fractional differential equations and k-generalized W-Hilfer fractional derivative. Suitable examples are given for justifying our results and addressing different specific cases of our problem. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of nonnegative solution to the following problem M(√R2n ∣u(x)-u(y)∣p/∣x-y∣n+ps dxdy) (-Δ)spu= f(x,u), in Ω, where n > sp with s ∊ (0,1), Ω. is an open bounded subset of Rn with Lipschitz boundary, M and f are two continuous functions, and (-Δ)sp is a fractional p-laplacian operator, our main tools are based on critical point theorems and the truncation technique. [ABSTRACT FROM AUTHOR]

We study the existence of weak solutions for a class of nonlinear differential equations with periodic boundary conditions and non-instantaneous impulse. The approach is based on a critical point theory. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of at least three positive solutions for a coupled system of Riemann-Liouville fractional order two-point boundary value problems, by using an Avery generalization of the Leggett-Williams fixed point theorem. And then, we establish the existence of at least 2k - 1 positive solutions to the fractional order boundary value problems for an arbitrary positive integer k. [ABSTRACT FROM AUTHOR]

In this paper we consider the class C of all T-periodic competitive and dissipative 3-dimensional systems which have a cyclic in the boundary and such that the origin is a source. We use the ideas in [1] in order to give a correct proof of theorem 1.2 of [1] where we study the coexistence state for these system. [ABSTRACT FROM AUTHOR]

This paper focuses on determining the eigenvalue intervals of λ1;λ2 and λ3 for the existence of at least one positive solution to a ternary system of Riemann-Liouville type p-Laplacian fractional order boundary value problems by utilizing a fixed point theorem on a cone under suitable conditions. [ABSTRACT FROM AUTHOR]

The aim of the paper is to develop monotone technique and its associated iterative scheme and apply it to prove existence results for nonlinear, weakly coupled system of Caputo fractional differential equations with nonlinear boundary conditions. [ABSTRACT FROM AUTHOR]

The mathematical modeling of non-linear boundary value problems of reaction diffusion systems for non-steady state conditions has been examined. In this analysis, the non-linear coupled partial differential equations are transformed into a system of ordinary differential equations and solved them analytically using Laplace transform technique to obtain temperature and concentration profiles. In this paper the thermodynamic coupling between heat and mass fluxes in the two industrial reaction diffusion systems of synthesis of vinyl chloride and dissociation of N2O reaction systems are analyzed. All the analytical results are compared with simulation results using Matlab. The numerical results agree with the appropriate theories. [ABSTRACT FROM AUTHOR]

This paper is aimed to formulate Campanato-type interior estimates for solutions of Rothe's approximate equations to parabolic partial differential systems in non-divergence form, "independently of the approximation." Combined with the estimates near the boundary in another paper, they will be applied to investigate the uniform Hölder continuity of first derivatives of the solution. [ABSTRACT FROM AUTHOR]

In this paper, using the operator theoretic techniques, we present some algorithms for the existence and approximation of the solutions for a couple of Dirichlet and Neumann nonlinear two point boundary value problems of ordinary second order hybrid differential equations. The proof of the main results rely on the Dhage iteration principle embodied in some recent hybrid fixed point theorems of Dhage(2014) in a partially ordered normed linear space. The approximation of solutions of the considered BVPs of ordinary nonlinear hybrid differential equations are obtained under certain mixed partial continuity and partial compactness type conditions. Some numerical examples are also provided to illustrate the validity of our hypotheses and the abstract results. [ABSTRACT FROM AUTHOR]

In this paper, we present an existence theorem of solution for a boundary value problem of a nonlinear integrodifferential equation of fractional order with integral boundary conditions by using measure of non compactness combined with fixed point theorem of Mönch. An example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper we consider a second order m-point boundary value problem for which we obtain the existence of multiple solutions by using Avery-Peterson Theorem with the introduction of new operator. In view of the mathematical characteristics that we observed, we write a new heuristic for multiple numerical solutions, which differs from the classical approach based on methods of fixed point. Finally, we perform numerical tests to validate our proposal. [ABSTRACT FROM AUTHOR]

Integral transforms have been introduced and found their application in certain boundary value problems. The Natural transform is closely connected to the Laplace and Sumudu transforms. In the present paper, we discuss the Natural transform on certain spaces of generalized functions. We obtain the Natural transform for a space of distributions and further investigate the cited transform on space of Boehmians. More results are also established. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem: {∇(∇up-2∇u) = f(x,u) + λg(x, u) in Ω u = 0 on ∂Ω, where Ω CN is an open bounded set with smooth boundary ∂Ω and λ ∈. Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and +∞, our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space W01,p(Ω) centered in the origin and with radius not dependent on λ. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of observability for distributed hyperbolic systems evolving in spatial domain Ω. It consists of the reconstruction of the initial conditions, on a subregion Γ of ∂Ω, that the initial state and speed are to be observed between two prescribed functions given only on the boundary subregion Γ. We give some definitions and properties of this kind of observability and we describe two approaches to solve this problem which the first is based on subdifferential techniques and the second one uses the Lagrangian multiplier method. This last approach leads to an algorithm which is implemented numerically and illustrated through an example and numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper we study a class of nonlinear elliptic problems under nonlocal Robin bound-ary conditions. We investigate the existence of generalised solutions and localise them by using fixed point methods and comparison principles. To make the results applicable, we provide methods that allow us to construct pairs of ordered lower and upper solutions. [ABSTRACT FROM AUTHOR]

The paper deals with Dichotomy, well conditioning of two-point boundary value problems on time scale dynamical systems using a suitable norm on Rn. The results presented in this paper on Dichotomy and well conditions of two-point boundary value problems unify both continuous and discrete systems and generalizes these results on time scale dynamical systems. We also present empirical validation of a set of theoretical-grounded metrics on object-oriented design. Fixed point theory on metric spaces is used as a tool to obtain the required object in object oriented designs and in designing flows. [ABSTRACT FROM AUTHOR]

In this paper the boundary value problem: {z" = ρ ⋅ g ⋅ z - p/γ. [1 + (zl)²]3/2 for x1 ≤ x ≤ x0 zl (x1) = - tan (π/2 - αg) zl (x0) = - tan αC z(x0 = 0 and z(x) is strictly decreasing on [x1, x0] is considered. Here: 0 < x1 < x0, ρ, g, γ p, α C, &alapha;g are constants having the following properties: ρ, g, γ, are strictly positive and 0 < π/2 - αg < α C < π/2. Necessary or sufficient conditions are given in terms of p for the existence of a concave solution of the above nonlinear boundary value problem. The static stability of the concave solution is proven. Numerical example is given. This kind of results can be useful in the experiment planning and technology design of single crystal sheet growth from the melt. With this aim this study was undertaken. [ABSTRACT FROM AUTHOR]

In this paper, we study Sturm-Liouville boundary value problems for second-order functional differential equations on infinite intervals [-τ +∞). By using the Leggett-Williams fixed point theorem, we obtain sufficient conditions for the existence of multiple positive solutions of the functional boundary value problem. [ABSTRACT FROM AUTHOR]

In the present paper the abstract nonlocal boundary value problem { du(t) / dt + Au(t) = f(t), (0 ≤ t ≤ 1), - d²u(t) / dt² + Au(t) = (t), (-1 ≤ t≤ 0), u(1) = u(-1) + μ for differential equations in a Hilbert space H, with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Holder spaces is established. The coercive stability estimates in Holder norms for solutions of the boundary value problems for elliptic-parabolic equations are obtained. [ABSTRACT FROM AUTHOR]

In this paper, via Schaeffer's theorem and Banach's fixed point theorem, we present some existence results of solutions for second order periodic boundary value problems for impulsive differential equations at fixed moments, [ABSTRACT FROM AUTHOR]

In this paper we use a transformation to convert the initial value problem x' = ƒ[sub1](t, x) + ƒ[sub2](t, x), x(O) = x[sub0], into one which fits within the framework of the unified monotone iterative technique, enabling us to use existing results to solve the given problem. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of solutions for some strongly nonlinear Dirichlet problems with natural growth condition on the non-linearity and L1 data in the context of Musielak spaces, we also give a proof of a Poincaré inequality in these spaces. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of boundary optimal control problems in this paper. We apply the controls through Neumann as well as Dirichlet data on the smooth part of the boundary where as homogeneous Neumann data is considered on the oscillating part of the boundary of the domain. We consider two cost functionals namely L²-cost functional and Dirichlet-cost functional. We apply periodic unfolding operator tools to establish corresponding limit optimal control problems. In the process we introduce interior and boundary unfolding operators to achieve the limit problems which consist two parts, namely in the lower part and the upper part with appropriate interface conditions. [ABSTRACT FROM AUTHOR]

In this paper, we use fixed point methods to study the boundary-value problems of non-linear fractional integro-differential equations with fractional boundary conditions. The existence of solutions are established by using the sufficient conditions. The main result is illustrated with an examples. [ABSTRACT FROM AUTHOR]

In this article, we present some results concerning the existence of weak solutions for a class of functional implicit fractional differential equations with multipoint boundary conditions. The main results are proved by applying Mönch's fixed point theorem associated with the technique of measure of weak noncompactness. [ABSTRACT FROM AUTHOR]

We investigate chaotic vibrations of flexible spherical rectangular shells loaded harmonically via the boundary conditions. In the first part of the paper we consider one-layer shell made from an isotropic and homogeneous material. The second part addresses non-linear dynamics of multi-layer shells, taking into account gaps between the layers (design non-linearity). Contact pressure between the layers was explicitly defined. Phase portraits, Fourier power spectra and wavelet spectra were constructed and investigated. In addition, an appropriate choice of the wavelets suitable to study the stated problem was made and validated. Analysis of the shell curvature and shell design non-linearity on the dynamical phenomena was carried out using also the phase difference as a new characteristic for monitoring and quantifying non-linear vibrations. [ABSTRACT FROM AUTHOR]

In this paper we give a brief survey of results dealing with the comparison principle and existence results for terminal-value problems (TVP). We begin with terminal differential inequalities, existence of extremal solutions and the corresponding comparison principle, for ordinary differential equations (ODE), and discuss the method of lower and upper solutions for ODE. We then present an important extension of this basic theory, which relaxes the strong assumption that v(t) ≤ u (t) for t ∈ [a, b], where v(t) and w(t) are lower and upper solutions, respectively. Next, we state results pertaining to TVP for impulsive ODE and then give parallel results for fractional differential equations. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of optimal boundary control problems associated with Laplacian posed on a domain having rapidly oscillating boundary. A rectangular region with oscillations on the top boundary is considered as a domain for simplicity. A control is applied on the regular bottom boundary part, away from the oscillatory one. We discuss both, Dirichlet as well as Neumann boundary control problem. In both of the cases the L²- cost functional is taken into account. A complete asymptotic analysis of the optimality system is obtained and then we derive appropriate error estimates. Homogenization is quite similar in both and is not very difficulty. But the major contribution of the work in this paper is the error analysis and we need to construct different test functions for Dirichlet and Neumann boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we extend the method of generalized quasilinearization to systems of degenerate singular perturbation problems. We construct, under suitable conditions, monotone sequences of lower and upper approximate solutions which converge uniformly and quadratically to the unique solution of the system of degenerate singular perturbation problems. [ABSTRACT FROM AUTHOR]

In this paper, the existence of at least three weak solutions for Navier problem {Δ(|Δu|Δu) = λf(x,u) + μg(x,u), in Ω, u = Δu = 0, on ∂Ω where Ω ⊂ ℝ² is non-empty bounded open set with smooth boundary ∂Ω, λ, μ ∈ [0, + ∞) and f, g : Ω x ℝ → ℝ are L¹-Carathéodory functions, is established. The approach is based on variational methods and critical points. [ABSTRACT FROM AUTHOR]

In this paper, using a three critical points theorem and variational methods, we study the existence of at least three weak solutions for a Neumann boundary value problem driven by a p-Laplacian operator. [ABSTRACT FROM AUTHOR]

Almost all the difficult mathematical problems arising in the applications are solved numerically. This is especially true for large size linear problems and for nonlinear ones. The main tools for the numerical treatment of problems on computers are appropriate codes which are highly sophisticated programs, able to solve specific classes of mathematical problems by only providing the essential data required by the problem itself. This last assertion implies that the user, often, needs not to know about the logical difficulties and the procedures which the codes are based on: the user is often required to do a little more than to push a button. Nevertheless, the role of numerical codes in the development of technology is a fundamental one. The main scope of this review paper is to give an idea of what is inside the codes and and to give an overview of the state of art not of the whole discipline, which is enormous, but only of the part of it concerning the codes for the solution of differential problems. [ABSTRACT FROM AUTHOR]

In this paper a theoretical procedure for the creation of a stable static droplike (concave) meniscus, appropriate for the growth of a single crystal ribbon (with specified half thickness), by edge-defined film-fed growth (EFG) technique, is presented. The method is based on explicit formulas, established as mathematical theorems, which locate the controllable part of the pressure difference across the free surface of the meniscus. In fact, the method consists in a set of calculus, which leads to the determination of the melt column height between the shaper top level and the crucible melt level in function of the pressure of the gas flow (introduced into the furnace for release the heat).The procedure is presented in general and it is numerically illustrated, revealing even situation when only convex-concave appropriate meniscus can be created. The novelty is that for the second order plan symmetric Young-Laplace equation three boundary conditions are specified (instead of two) and that value of the controllable part of the pressure difference is found for which the boundary conditions are satisfied. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions of boundary value problems for first order nonresonance impulsive functional dynamic inclusions on time scales. By using suitable fixed point theorems, we study the cases when the multivalued map has convex and non-convex values. [ABSTRACT FROM AUTHOR]

In this paper the following two nonlinear botlndaly value problems are considered: z'e = rho; · g · Ze - pe [1 + (z'e)²]3/2 - 1/r · [1 + (z'e)²] z'e, r ∈ [re, Rge], z'e(re) = - tan(φ/2 - αg); z;e(Rge) = - tan αc; ze (Rge) = 0. ze(r) is strictly decreasing on [re, · Rge]. z"i = ρ · g · zi/γ [1 + (z'i)²]3/2 - 1/r · [1 + i]²] · z'i, r ε [Rge, ri], z'i(Rgi) = tanαc; z'i(ri) = tan(φ/2- αg); z1(Rgi) = O, zi(r) is strictly increasing on [Rgi, ri]. Here; 0 < Rgi < ri ≤ rgi + Rge/2 ≤ re < < Rge; ρ, g, γ pe, pi, αc,αg are constants having the following properties: ρ, g, γ are strictly positive and 0 < φ/2 - αg < αc < φ/2. Necessary or sufficient conditions are given, in terms of pc, pi for the existence of a concave solution of the above nonlinear boundary value problems (ul.b.v.p.). This kind of results can be useful in experiment planing and manufacturing technology design of single-crystal tube growth from, the melt. With this aim this study was undertaken. [ABSTRACT FROM AUTHOR]