Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908833941553152 |
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| author | Bhowmick, Souvik Ghosh, Sekhar Kumar, Vishvesh |
| author_facet | Bhowmick, Souvik Ghosh, Sekhar Kumar, Vishvesh |
| contents | This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak solutions using a variational framework combining a truncation argument with the notion of genus. A central part of our analysis is the verification of the Palais--Smale (PS) condition for the associated energy functional for every $q \in (1, p_{s_\sharp}^*)$, despite the challenges posed by the lack of compactness due to the critical exponent. The results obtained in the paper are new even in the classical case $p = 2$, highlighting the broader applicability of the methods developed here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent Bhowmick, Souvik Ghosh, Sekhar Kumar, Vishvesh Analysis of PDEs 35M12, 35J60, 35R11, 35B33, 35A15 This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak solutions using a variational framework combining a truncation argument with the notion of genus. A central part of our analysis is the verification of the Palais--Smale (PS) condition for the associated energy functional for every $q \in (1, p_{s_\sharp}^*)$, despite the challenges posed by the lack of compactness due to the critical exponent. The results obtained in the paper are new even in the classical case $p = 2$, highlighting the broader applicability of the methods developed here. |
| title | Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent |
| topic | Analysis of PDEs 35M12, 35J60, 35R11, 35B33, 35A15 |
| url | https://arxiv.org/abs/2506.11832 |