Nonlinear Schrodinger equations near an infinite well potential

被引：5

作者：

Bartsch, Thomas ^{[1
]}

Parnet, Mona ^{[1
]}

机构：

[1] Univ Giessen, Math Inst, D-35392 Giessen, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 51卷 / 1-2期

关键词：

SIGN-CHANGING SOLUTIONS; MULTI-BUMP SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC PROBLEMS; NODAL SOLUTIONS; CRITICAL GROWTH; BOUND-STATES; MULTIPLICITY; EXISTENCE; PROFILE;

D O I：

10.1007/s00526-013-0678-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper deals with standing wave solutions of the dimensionless nonlinear Schrodinger equation where the potential is close to an infinite well potential , i. e. on an exterior domain , , and as in a sense to be made precise. The nonlinearity may be of Gross-Pitaevskii type. A standing wave solution of with vanishes on and satisfies Dirichlet boundary conditions, hence it solves We investigate when a standing wave solution of the infinite well potential gives rise to nearby solutions of the finite well potential with large. Considering as a singular limit of we prove a kind of singular continuation type results.

引用

页码：363 / 379

页数：17

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