MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM

作者：Fang Yanqin^*; Zhang Jihui

来源：Communications on Pure and Applied Analysis, 2011, 10(4): 1267-1279.

DOI：10.3934/cpaa.2011.10.1267

• Schrodinger-Maxwell
• Ljusternik-Schnirelmann theory
• multiple solutions

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.

• 出版日期2011-7
• 单位南京师范大学