in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.

This study focuses on nonlocal boundary value problems (BVP) for linear and nonlinear elliptic differential-operator equations (DOE) that are defined in Banachvalued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal Lpregularity and Fredholmness of linear BVP, uniformly with respect to this parame...

We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.

A weighted least squares method is given for the numerical solution of elliptic partial differential equations of Agmon-Douglis-Nirenberg type and an error analysis is provided. Some examples are given.

Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.

I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side...

This paper aims to show the existence of nontrivial solutions for discrete elliptic boundary value problems by using the “Mountain Pass Theorem”. Some conditions are obtained for discrete elliptic boundary value problems to have at least two nontrivial solutions. The results obtained improve the consequences of the known literature [Guang Zhang, Existence of nontrivial solutions for discrete el...

Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for ...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...

With the aid of symbolic computation, a new extended Jacobi elliptic function expansionmethod is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function s...