Multiplicity of solutions for a singular system with sign-changing potential

This paper focuses on a singular system with a sign-changing potential in Γ, a bounded domain with a Lipschitz boundary in . By imposing appropriate conditions on the weight potential, which is allowed to change sign, we establish the existence of multiple solutions using the shape optimization appr...

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Bibliographic Details
Published inForum mathematicum Vol. 36; no. 6; pp. 1499 - 1515
Main Authors Lin, Wentao, Wei, Yilan
Format Journal Article
LanguageEnglish
Published De Gruyter 01.09.2024
Subjects
34B10
35A15
35J35
35J60
35Q82
46E35
multiple solution
sign-changing potential
The singular system
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Summary:This paper focuses on a singular system with a sign-changing potential in Γ, a bounded domain with a Lipschitz boundary in . By imposing appropriate conditions on the weight potential, which is allowed to change sign, we establish the existence of multiple solutions using the shape optimization approach. This study represents one of the earliest endeavors to explore and analyze the occurrence of multiple solutions in fractional singular systems involving sign-changing potentials. By explicitly addressing this particular aspect, our paper contributes significantly to the limited body of literature that exists in this specific field.
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2023-0345