Nontrivial weak solutions for nonlocal nonhomogeneous elliptic problems

Abstract

This article concerns the following class of nonlocal nonhomogeneous elliptic problems: where Ω is a bounded domain of , α, , is a matrix with variable coefficients and is a positive function which are defined almost everywhere with respect to the variable x. By using the Schauder and Tychonoff fixed-point theorems, we establish two existence theorems of weak solutions for this problem according to two bundles of hypotheses on α, β and g.