On double phase Kirchhoff problems with singular nonlinearity

In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data, we prove the existence of at least two weak solutions that ha...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 12; no. 1; pp. 1079 - 1106
Main Authors Arora, Rakesh, Fiscella, Alessio, Mukherjee, Tuhina, Winkert, Patrick
Format Journal Article
LanguageEnglish
Published De Gruyter 14.06.2023
Subjects
35A15
35J15
35J60
35J62
35J75
double phase operator
fibering method
Kirchhoff term
multiple solutions
Nehari manifold
singular problems
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Summary:In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions on the data, we prove the existence of at least two weak solutions that have different energy sign. Our treatment is based on the fibering method in form of the Nehari manifold. We point out that we cover both the nondegenerate as well as the degenerate Kirchhoff case in our setting.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2022-0312