An existence result for (p, q)-Laplace equations involving sandwich-type and critical growth

Abstract

We investigate the existence of a nontrivial nonnegative solution to (p, q)-Laplace equations involving two nonlinear terms, one grows as s with q < s < p and the other possibly has critical growth. This interesting case cannot be appeared in single m-Laplace equations and has not been studied under even the subcritical growth. Our argument is based on the concentration?compactness principle by P.L. Lions and the Ekeland variational principle.