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.