Asymptotically linear Schrödinger–Poisson systems with potentials vanishing at infinity
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- 作者：Hongbo Zhua ; snoviezhbxw@163.com
- 关键词：Schrö ; dinger– ; Poisson system ; Vanishing potential ; Bound state
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2011
- 出版时间：15 August 2011
- 年：2011
- 卷：380
- 期：2
- 页码：501-510
- 全文大小：181 K
文摘
In this paper, we are concerned with the following nonlinear Schrödinger–Poisson equations () where λ>0 is a parameter, the potential V(x) may be vanishing at infinity, f(s) is asymptotically linear at infinity, that is f(s)O(s) as s→∞. For this kind of potential, it seems difficult to find solutions in . Under some assumptions on V(x),K(x) and f(s), we prove that problem (aaaa) has a positive solution for λ small and has no any nontrivial solution for λ large.