| Autor: |
Xia Su, Chunhua Deng |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 12, Pp 30487-30500 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231557?viewType=HTML |
| Popis: |
In this paper, we consider the following semilinear Schrödinger equation: $ \begin{eqnarray*} \left\{ \begin{array}{ll} -\Delta u+V(x)u = a(x)g(u)&{\mbox{for}}\; x\in \mathbb{R}^{N} ,\\ u(x)\rightarrow0&{\mbox{as}}\; |x|\rightarrow \infty , \end{array} \right. \end{eqnarray*} $ where $ a(x) > 0 $ for all $ \mathbb{R}^{N} $. Under some different superlinear conditions on $ g(u) $, we obtain the existence of solutions for the above problem. In order to regain the compactness of the Sobolev embedding, a competing condition between $ a(x) $ and $ V(x) $ is introduced. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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