On nonlinear Schrodinger-Poisson equations with general potentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Seok, Jinmyoung

关键词: Nonlinear;    Schrodinger-Poisson equations;    Variational methods;   

DOI  :  10.1016/j.jmaa.2012.12.054

来源: Elsevier

【 摘 要 】

We study the existence of infinitely many finite energy radial solutions to the nonlinear Schrodinger-Poisson equations {Delta u - u - phi(x)u + f (u) = 0 in R-3 Delta phi + u(2) = 0, lim(\x\-->infinity) phi(x) = 0 in R-3 (NSPE for short) under some structure conditions on the nonlinearity function f. As consequences of the main result, we can provide examples of f which guarantee the existence of infinitely many finite energy solutions but (i) f (t) grows faster than t(2) and slower than t(p) for all p > 2 or (ii) f (t) is the same as \t\t when \t\ <= t(0) for arbitrarily given t(0) > 0. If f (t) = \t\(p-1)t, it is known that (NSPE) admits no finite energy nontrivial solutions when p is an element of (1, 2] and admits infinitely many finite energy solutions when p is an element of (2, 5) so examples (i) and (ii) show some interesting features of (NSPE). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free