Eigenvalues of an Operator Homogeneous at the Infinity - 10.5269/bspm.v28i1.10815

Abstract

In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study the solvability of the problem \mathcal{A}u = -div (A(x,\nabla u)) = f(x,u) + h,  in  \Omega, u=0  on \partial \Omega, as well as the spectrum of G_0'(u)= \lambda m |u|^{p-2}u  in  \Omega, u=0  on \partial \Omega.