MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM

被引：5

作者：

Fang, Yanqin ^{[1
]}

Zhang, Jihui ^{[1
]}

机构：

[1] Nanjing Normal Univ, Jiangsu Key Lab NSLSCS, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 04期

关键词：

Schrodinger-Maxwell; Ljusternik-Schnirelmann theory; multiple solutions; POSITIVE SOLUTIONS; POISSON PROBLEM; SEMICLASSICAL STATES; BOUND-STATES; EQUATIONS; POTENTIALS; MOLECULES; SPHERES; WAVES; ATOMS;

D O I：

10.3934/cpaa.2011.10.1267

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following system -epsilon(2)Delta v + V(x)v + psi(x)v = v(p), x is an element of R(3), -Delta psi = 1/epsilon v(2), lim(vertical bar x vertical bar -> infinity)psi(x) = 0, x is an element of R(3), where epsilon > 0, p is an element of (3, 5), V is positive potential. We relate the number of solutions with topology of the set where V attain their minimum value. By applying Ljusternik-Schnirelmann theory, we prove the multiplicity of solutions.

引用

页码：1267 / 1279

页数：13

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