Constant sign and nodal solutions for superlinear double phase problems

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...

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Bibliographic Details
Published inAdvances in calculus of variations Vol. 14; no. 4; pp. 613 - 626
Main Authors Gasiński, Leszek, Papageorgiou, Nikolaos S.
Format Journal Article
LanguageEnglish
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
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Summary: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 negative solution and a nodal solution. The nodal solution has exactly two nodal domains.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1864-8258
1864-8266
DOI:10.1515/acv-2019-0040