A positive solution of asymptotically periodic Schrödinger equations with local superlinear nonlinearities
| Autor: | Chun-Lei Tang, Yong-Yong Li, Gui-Dong Li |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Electronic Journal of Qualitative Theory of Differential Equations, Vol 2020, Iss 30, Pp 1-15 (2020) |
| ISSN: | 1417-3875 |
| Popis: | In this paper, we investigate the following Schrödinger equation \begin{equation*} -\Delta u+V(x)u=\lambda f(u) \quad {\rm in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$, $\lambda>0$, $V$ is an asymptotically periodic potential and the nonlinearity term $f(u)$ is only locally defined for $|u|$ small and satisfies some mild conditions. By using Nehari manifold and Moser iteration, we obtain the existence of positive solutions for the equation with sufficiently large $\lambda$. |
| Databáze: | OpenAIRE |
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