Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918035349045248 |
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| author | Böer, Eduardo de Souza Miyagaki, Olímpio Hiroshi Pucci, Patrizia |
| author_facet | Böer, Eduardo de Souza Miyagaki, Olímpio Hiroshi Pucci, Patrizia |
| contents | In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})Δu +Q(x)u + μ(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ μ>0 $, $ V $ a sign-changing and possible unbounded potential, $ Q $ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12472 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential Böer, Eduardo de Souza Miyagaki, Olímpio Hiroshi Pucci, Patrizia Analysis of PDEs 35J60, 35J15, 35Q55, 35B25 In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})Δu +Q(x)u + μ(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ μ>0 $, $ V $ a sign-changing and possible unbounded potential, $ Q $ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case. |
| title | Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential |
| topic | Analysis of PDEs 35J60, 35J15, 35Q55, 35B25 |
| url | https://arxiv.org/abs/2207.12472 |