Existence and multiplicity of solutions for a new p(x)-Kirchhoff problem with variable exponents

In this article, we study a class of new )-Kirchhoff problem without satisfying the Ambrosetti-Rabinowitz type growth condition. Under some suitable superliner conditions, we introduce new methods to show the boundedness of Cerami sequences. By using the mountain pass lemma and the symmetric mountai...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2023-01, Vol.21 (1), p.1383-1406
Main Authors: Chu, Changmu, Xie, Yanling, Zhou, Dizhi
Format: Article
Language:English
Subjects:
35A15
35J60
Cerami sequences
infinitely many solutions
Kirchhoff problem
mountain pass lemma
Mountains
p(x)-kirchhoff problem
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Summary:In this article, we study a class of new )-Kirchhoff problem without satisfying the Ambrosetti-Rabinowitz type growth condition. Under some suitable superliner conditions, we introduce new methods to show the boundedness of Cerami sequences. By using the mountain pass lemma and the symmetric mountain pass lemma, we prove that the )-Kirchhoff problem has a nontrivial weak solution and infinitely many solutions.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2022-0520