Nonlinear elliptic problems in weighted variable exponent Sobolev spaces by topological degree

Abstract

In this paper, we prove the existence of solutions for the nonlinear p(·)-degenerate problems involving nonlinear operators of the form − div a(x, ∇u) = f(x, u, ∇u) where a and f are Caratheodory functions satisfying some nonstandard growth conditions.