Two solutions for Dirichlet double phase problems with variable exponents

This paper is devoted to the study of a double phase problem with variable exponents and Dirichlet boundary condition. Based on an abstract critical point theorem, we establish existence results under very general assumptions on the nonlinear term, such as a subcritical growth and a superlinear cond...

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Bibliographic Details
Published inAdvanced nonlinear studies Vol. 24; no. 3; pp. 734 - 747
Main Authors Amoroso, Eleonora, Bonanno, Gabriele, D’Aguì, Giuseppina, Winkert, Patrick
Format Journal Article
LanguageEnglish
Published De Gruyter 01.07.2024
Subjects
35A01
35B33
35D30
35J62
35J66
bounded solutions
critical point theory
double phase operator with variable exponents
multiplicity results
superlinear reaction
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ISSN2169-0375
2169-0375
DOI10.1515/ans-2023-0134

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Summary:This paper is devoted to the study of a double phase problem with variable exponents and Dirichlet boundary condition. Based on an abstract critical point theorem, we establish existence results under very general assumptions on the nonlinear term, such as a subcritical growth and a superlinear condition. In particular, we prove the existence of two bounded weak solutions with opposite energy sign and we state some special cases in which they turn out to be nonnegative.
ISSN:2169-0375
2169-0375
DOI:10.1515/ans-2023-0134