Solutions for fractional p(x,⋅)-Kirchhoff-type equations in RN

In this paper, we discuss the fractional p ( x , ⋅ ) -Kirchhoff-type equations M ( ∫ R N × R N 1 p ( x , y ) | u ( x ) − u ( y ) | p ( x , y ) | x − y | N + s p ( x , y ) d x d y ) ( − Δ p ( x , . ) ) s u + | u | p ¯ ( x ) − 2 u = f ( x , u ) . We weaken the conditions on the nonlinear term f and ge...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2024; no. 1; p. 123
Main Author Wan, Lili
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2024
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
Theorems
Variational methods
Mountain pass lemma
Kirchhoff-type equations
46E35
35R11
Fractional
Symmetric mountain pass lemma
35J35
35S15
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Summary:In this paper, we discuss the fractional p ( x , ⋅ ) -Kirchhoff-type equations M ( ∫ R N × R N 1 p ( x , y ) | u ( x ) − u ( y ) | p ( x , y ) | x − y | N + s p ( x , y ) d x d y ) ( − Δ p ( x , . ) ) s u + | u | p ¯ ( x ) − 2 u = f ( x , u ) . We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1025-5834
1029-242X
DOI:10.1186/s13660-024-03204-3