Nonlinear Elliptic Equation With Nonlocal Integral Boundary Condition Depending on Two Parameters

Abstract

In this paper, the two-dimensional nonlinear elliptic equation with the boundary integral condition depending on two parameters is solved by finite difference method. The main aim of this paper is to investigate the conditions under those all eigenvalues of corresponding difference eigenvalue problem are positive. For this purpose, we investigate the spectrum structure of one-dimensional difference eigenvalue problem with integral condition. In particular, conditions of the existence and some properties of negative eigenvalue are analyzed in details.

On the Spectrum Structure for One Difference Eigenvalue Problem With Nonlocal Boundary Conditions

“…As separate mathematical task the difference eigenvalue problem with nonlocal conditions was investigated in [2,23,28] (see also the review article [30]). Some recent results are presented in the papers [2,5,10,20,21,29,31,33].…”

Existence of multiple positive solutions for a third-order boundary value problem with nonlocal conditions

“…In [11], the author proves the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with a nonlinear term having derivative dependence. In [6], the authors solve the two-dimensional nonlinear elliptic equation with the boundary integral condition depending on two parameters. The next reason is that namely positive solutions to boundary value problems frequently occur in applications.…”