Multiplicity results for double phase problems involving a new type of critical growth

• Published in: Journal of mathematical analysis and applications Vol. 530; no. 1; p. 127659
• Main Authors: Ha, Hoang Hai, Ho, Ky
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2024
• Subjects: Concentration-compactness principle; Critical embeddings; Double phase operators; Variable exponent spaces; Variational methods; Double phase operators; Concentration-compactness principle; Variable exponent spaces; Variational methods; Critical embeddings
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2023.127659

Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared to previous works on the subject. In order to overcome the lack of compactness caused by the critical exponents, we establish a concentration-compactness principle of Lions type for spaces associated with double phase operators, which is of independent interest to us. Our results are new, even in the case of constant exponents.