Sign changing solutions for critical double phase problems with variable exponent
Nikolaos S. Papageorgiou
National Technical University of Athens, GreeceFrancesca Vetro
Palermo, ItalyPatrick Winkert
Technische Universität Berlin, Germany
Abstract
In this paper, we deal with a double phase problem with variable exponent and a right-hand side consisting of a Carathéodory perturbation defined only locally and of a critical term. We stress that the presence of the critical term inhibits the possibility to apply results of the critical point theory to the corresponding energy functional. Instead, we use suitable cut-off functions and truncation techniques in order to work with a coercive functional. Then, using variational tools and an appropriate auxiliary coercive problem, we can produce a sequence of sign changing solutions to our main problem converging to in and in the Musielakk–Orlicz Sobolev space.
Cite this article
Nikolaos S. Papageorgiou, Francesca Vetro, Patrick Winkert, Sign changing solutions for critical double phase problems with variable exponent. Z. Anal. Anwend. 42 (2023), no. 1/2, pp. 235–251
DOI 10.4171/ZAA/1731