Semiclassical states for the nonlinear Schrodinger equation on saddle points of the potential via variational methods

被引：35

作者：

d'Avenia, Pietro ^{[2
]}

Pomponio, Alessio ^{[2
]}

Ruiz, David ^{[1
]}

机构：

[1] Univ Granada, Fac Ciencias, Dpto Anal Matemat, E-18071 Granada, Spain

[2] Politecn Bari, Dipartimento Matemat, I-70125 Bari, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 10期

关键词：

Nonlinear Schrodinger equation; Semiclassical states; Variational methods; CONCENTRATION-COMPACTNESS PRINCIPLE; SEMILINEAR ELLIPTIC PROBLEMS; SCALAR FIELD-EQUATIONS; POSITIVE SOLUTIONS; STANDING WAVES; BOUND-STATES; EXISTENCE; CALCULUS;

D O I：

10.1016/j.jfa.2012.03.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study semiclassical states for the problem -epsilon(2) Delta u + V(x)u = f (u) in N, where f (u) is a superlinear nonlinear term. Under our hypotheses on f. a Lyapunov-Schmidt reduction is not possible. We use variational methods to prove the existence of spikes around saddle points of the potential V (x). (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：4600 / 4633

页数：34

共 32 条

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