| Autor: |
Senli Liu, Haibo Chen, Zhaosheng Feng |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Electronic Journal of Differential Equations, Vol 2020, Iss 130,, Pp 1-17 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
In this article we study the Schrodinger-Poisson system $$\displaylines{ -\Delta u +V(|x|)u+\lambda\phi u = f(u), \quad x\in\mathbb{R}^3, \cr -\Delta \phi =u^2, \quad x\in\mathbb{R}^3, }$$ where V is a singular potential with the parameter $\alpha$ and the nonlinearity f satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when $\lambda=0$. By the perturbation method, we obtain a nontrivial solution to above system when $\lambda\neq 0$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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