Existence and multiplicity results for the zero mass Schrödinger-Bopp-Podolsky system with critical growth
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909870959099904 |
|---|---|
| author | Huang, Wentao Wang, Li |
| author_facet | Huang, Wentao Wang, Li |
| contents | In this paper we study the following zero mass Schrödinger-Bopp-Podolsky system with critical growth \[ \begin{cases} -Δu +q^2ϕu=μ|u|^{p-2}u+|u|^4u\\ -Δϕ+a^2Δ^2ϕ=4πu^2, \end{cases} \] where $a>0$, $q\neq0$, $μ>0$ is a parameter and $p\in(3,6)$. By introducing a new functional framework developed by Caponio et al. \cite{Cd}, we first establish the existence of positive ground state solutions for the case of $p\in(3,6)$. Moreover, for the case of $p\in(4,6)$, multiplicity results are obtained by applying an abstract critical point theorem due to Perera \cite{Pe}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23266 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and multiplicity results for the zero mass Schrödinger-Bopp-Podolsky system with critical growth Huang, Wentao Wang, Li Analysis of PDEs In this paper we study the following zero mass Schrödinger-Bopp-Podolsky system with critical growth \[ \begin{cases} -Δu +q^2ϕu=μ|u|^{p-2}u+|u|^4u\\ -Δϕ+a^2Δ^2ϕ=4πu^2, \end{cases} \] where $a>0$, $q\neq0$, $μ>0$ is a parameter and $p\in(3,6)$. By introducing a new functional framework developed by Caponio et al. \cite{Cd}, we first establish the existence of positive ground state solutions for the case of $p\in(3,6)$. Moreover, for the case of $p\in(4,6)$, multiplicity results are obtained by applying an abstract critical point theorem due to Perera \cite{Pe}. |
| title | Existence and multiplicity results for the zero mass Schrödinger-Bopp-Podolsky system with critical growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.23266 |