On critical double phase problems in R N involving variable exponents

Abstract

We establish a Lions-type concentration-compactness principle and its variant at infinity for Musielak-Orlicz-Sobolev spaces associated with a double phase operator with variable exponents. Based on these principles, we demonstrate the existence and concentration of solutions for a class of critical double phase equations of Schrödinger type in RN involving variable exponents with various types of potentials. Our growth condition is more appropriately suited compared to the existing works.