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.
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页码：1267 / 1279
页数：13
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