Existence of radial solutions for a class of p(x)-laplacian equations with critical growth

Abstract

Using variational methods we establish the existence of solutions for the following class of p(x)-Laplacian equations: -div (|∇u|p(x)-2 ∇u) + |u|p(x)-2 u= λ|q(x)-2 u + |u| p(x)-2 u, ℝN (P) where λ (0, ∞) is a parameter and p(x),q(x): ℝ → ℝ are radial continuous functions satisfying 1 < p(x) < N and p(x) << q(x)