Asymptotically linear Schrodinger-Poisson systems with potentials vanishing at infinity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

Zhu, Hongbo

关键词: Schrodinger-Poisson system;    Vanishing potential;    Bound state;   

DOI  :  10.1016/j.jmaa.2010.09.071

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the following nonlinear Schrodinger-Poisson equations {-Delta u + V(x)u + lambda phi(x)u = k(x)f(u), x is an element of R-3, -Delta phi = u(2), lim(vertical bar x vertical bar ->infinity) phi(x) = 0, where lambda > 0 is a parameter, the potential V(x) may be vanishing at infinity, f(s) is asymptotically linear at infinity, that is f(s) similar to O(s) as s -> infinity. For this kind of potential, it seems difficult to find solutions in H-1(R-3). Under some assumptions on V(x), K(x) and f(s), we prove that problem (P) has a positive solution for lambda small and has no any nontrivial solution for lambda large. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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