Nonlinear perturbations of a $p(x)$-Laplacian equation with critical growth in ${\mathbb{R}}^N$

Abstract

We prove the existence of solution for a class of $p(x)$-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.

To appear in Mathematische Nachrichten

References in corpus (1)

• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids