arXiv:2305.17859 Abstract | arXiv Analytics

arXiv:2305.17859 [math.AP]Abstract References Reviews Resources

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

Published 2023-05-29Version 1

Using variational methods, we have obtained 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 address the lack of compactness caused by the critical exponents, we establish a concentration-compactness principle of Lions type for spaces involving double phase operators, which is of independent interest to us. Our results are novel, even in the case of constant exponents.

Categories: math.AP

Subjects: 35B33, 35D30, 35J20, 49J35, 35J60, 46E35

Keywords: double phase problems, critical growth, multiplicity results, variational methods, double phase operators

Related articles: Most relevant | Search more

arXiv:2006.02410 [math.AP] (Published 2020-06-03)

On a $p(\cdot)$-biharmonic problem of Kirchhoff type involving critical growth

Nguyen Thanh Chung, Ky Ho

arXiv:1906.01924 [math.AP] (Published 2019-06-05)

Double phase problems and a discontinuity property of the spectrum

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

arXiv:1810.07995 [math.AP] (Published 2018-10-18)

Double phase problems with variable growth