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.