NONTRIVIAL SOLUTIONS FOR A MIXED BOUNDARY PROBLEM FOR SCHRODINGER EQUATIONS WITH AN EXTERNAL MAGNETIC FIELD

被引：4

作者：

Alves, Claudianor O. ^{[1
]}

Nemer, Rodrigo C. M. ^{[1
]}

Soares, Sergio H. M. ^{[2
]}

机构：

[1] Univ Fed Campina Grande, Unidade Acad Matemat & Estat, BR-58109970 Campina Grande, PB, Brazil

[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2015年 / 46卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Nonlinear Schrodinger equation; variational methods; Lusternik-Schnirelman category; Morse theory; MULTIPLE POSITIVE SOLUTIONS; NLS EQUATIONS; ELECTROMAGNETIC-FIELDS; ELLIPTIC PROBLEMS; STATES; EXISTENCE; NUMBER;

D O I：

10.12775/TMNA.2015.050

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of solutions for a class of nonlinear Schrodinger equations involving a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lusternik-Shnirelman category and the Morse theory to estimate the number of nontrivial solutions in terms of the topology of the part of the boundary where the Neumann condition is prescribed.

引用

页码：329 / 362

页数：34

共 36 条

[1] Solutions to nonlinear Schrodinger equations with singular electromagnetic potential and critical exponent [J].