Constant sign and nodal solutions for superlinear double phase problems

• Published in: Advances in calculus of variations Vol. 14; no. 4; pp. 613 - 626
• Main Authors: Gasiński, Leszek, Papageorgiou, Nikolaos S.
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.10.2021; Walter de Gruyter GmbH
• Subjects: 35D05; 35J60; constant sign and nodal solutions; Dirichlet problem; Nehari manifold, Musielak–Orlicz–Sobolev spaces; superlinear reaction; Unbalanced double phase operator

We consider a double phase problems with unbalanced growth and a superlinear reaction, which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools and the Nehari method, we show that the Dirichlet problem has at least three nontrivial solutions, a positive solution, a negativ...