Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system

Authors

Yanqin Fang, University of WollongongFollow
Jihui Zhang, Nanjing Normal University

RIS ID

112134

Publication Details

Fang, Y. & Zhang, J. (2011). Multiplicity of solutions for the nonlinear Schrödinger-Maxwell system. Communications on Pure and Applied Analysis, 10 (4), 1267-1279.

Abstract

In this paper, we study the following system -ε2v + V (x)v + ψ(x)v = vp, x ε R3, -Δψ=1/εv 2,lim |ψ|(x)=0, x ε R3, where ε ≥ 0, p ε (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.