The dual variational method for n-th order ODEs with multipoint boundary conditions

We discuss the eigenvalue problem for n-th order equations with multipoint boundary conditions. We present the variational method in spite of the fact that the nonlinearity is dependent on the derivative of n/2 order. The results can be applied applied to both sublinear and superlinear cases.     

Positive solutions for systems of nonlinear second‐order multipoint boundary value problems

We study the existence of positive solutions for systems of second‐order nonlinear ordinary differential equations, subject to multipoint boundary conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

Bifurcation from trivial solution for elliptic systems with nonlinear boundary conditions

In this paper, we investigate semilinear elliptic systems having a parameter with nonlinear Neumann boundary conditions over a smooth bounded domain. The objective of our study is to analyse bifurcation component of positive solutions from trivial solution and their stability. The results are obtained via classical bifurcation theorem from a simple eigenvalue, by studying the eigenvalue problem of elliptic systems.     

Sixth‐order Cahn–Hilliard systems with dynamic boundary conditions

Our aim in this paper is to define dynamic boundary conditions for several sixth‐order Cahn–Hilliard systems. We then study the well‐posedness and the dissipativity of the systems derived. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions

In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions. By constructing the Poincare operator, we obtain the existence of -periodic weak solutions under some reasonable assumptions.     

Nontrivial solutions for asymptotically linear hamiltonian systems with Lagrangian boundary conditions

In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.     

Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions.     

First order differential equations with piecewise constant arguments and nonlinear boundary value conditions

This paper is devoted to the study of differential equations with piecewise constant arguments coupled with nonlinear boundary value conditions. Under suitable assumptions on the data of the equation, by means of the method of (weakly coupled) lower and upper solutions, we derive the existence of extremal solutions and extremal quasi-solutions. Moreover some results are given concerning the uniqueness of solutions. Furthermore, we deduce some maximum principles related to the linear equation which allow us to develop the monotone iterative method. Some illustrative examples are also presented.     

Fractional order nonlinear mixed coupled systems with coupled integro-differential boundary conditions

We study the existence and uniqueness of solutions for a class of coupled fractional differential equations involving both Riemann-Liouville and Caputo fractional derivatives, and coupled integro-differential boundary conditions. We derive the desired results with the aid of modern methods of functional analysis. An example illustrating the abstract results is also presented.     

Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type

The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd.     

First order functional differential equations with periodic boundary conditions

In this article, the authors prove an existence theorem for periodic boundary value problems for first order functional differential equations (FDE) in Banach algebras under mixed generalized Lipschitz and Carathéodory conditions. The existence of extremal positive solutions is also proved under certain monotonicity conditions. An example illustrating the results is included.     

Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions

Using the theory of fixed point index, we discuss the existence and multiplicity of nonnegative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate in an example that all the constants that occur in our theory can be computed. Copyright © 2013 John Wiley & Sons, Ltd.     

A second‐order linearized difference scheme on nonuniform meshes for nonlinear parabolic systems with Neumann boundary value conditions

A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Neumann boundary value problem of a nonlinear parabolic system. It is proved that the difference scheme is uniquely solvable and second‐order convergent in L_∞‐norm. A numerical example is given. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 230–247, 2004     

Time delayed parabolic systems with coupled nonlinear boundary conditions

The aim of this paper is to show the existence and uniqueness of a solution for a system of time-delayed parabolic equations with coupled nonlinear boundary conditions. The time delays are of discrete type which may appear in the reaction function as well as in the boundary function. The approach to the problem is by the method of upper and lower solutions for nonquasimonotone functions.

     

Partial reconstruction of the source term in a linear parabolic initial problem with first order boundary conditions

We consider the inverse problem of identifying a factor in the source term of a parabolic mixed system with first-order boundary conditions. The supplementary information, which is needed to do it, is given by the knowledge of the evolution in time of a certain integral with respect to a suitable Borel measure.     

Second order problems with functional conditions including Sturm–Liouville and multipoint conditions

In this paper we study the solvability of equations of the form ‐(d/dt)φ (t, u, u (t), u ′(t)) = f (t, u, u (t), u ′(t)) for a.e. t ∈ I = [a, b ], together with functional‐boundary conditions which cover, amongst others, Sturm–Liouville and multipoint boundary data as particular cases. Our approach uses upper and lower solutions together with growth restrictions of Nagumo's type. An example is presented to show the applicability of the obtained results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complete second order differential equations in Banach spaces with dynamic boundary conditions

In this paper, we deal with the mixed initial boundary value problem for complete second order (in time) linear differential equations in Banach spaces, in which time-derivatives occur in the boundary conditions. General wellposedness theorems are obtained (for the first time), which are used to solve the corresponding inhomogeneous problems. Examples of applications to initial boundary value problems for partial differential equations are also presented.