Semi-classical states for the Choquard equation

被引：163

作者：

Moroz, Vitaly ^{[1
]}

Van Schaftingen, Jean ^{[2
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain, Belgium

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 52卷 / 1-2期

关键词：

NONLINEAR SCHRODINGER-EQUATIONS; STANDING WAVES; CRITICAL FREQUENCY; BOUND-STATES; EXISTENCE; DECAY;

D O I：

10.1007/s00526-014-0709-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the nonlocal equation where , , is the Riesz potential and is a small parameter. We show that if the external potential has a local minimum and then for all small the problem has a family of solutions concentrating to the local minimum of provided that: either , or and , or and . Our assumptions on the decay of and admissible range of are optimal. The proof uses variational methods and a novel nonlocal penalization technique that we develop in this work.

引用

页码：199 / 235

页数：37

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