On critical double phase problems in R N involving variable exponents

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 Schr & ouml;dinger type in R N involving variable exponents with various types of potentials. Our growth condition is more appropriately suited compared to the existing works. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.