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.
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页码：199 / 235
页数：37
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