Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2017-01-01

Journal: ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Included Journals: SCIE、ESI高被引论文

Issue: 12

Page Number: 1-23

ISSN: 1417-3875

Key Words: quasilinear Schrodinger system; critical growth; standing wave solutions; mountain pass theorem; (PS)(c) sequence

Abstract: This paper is concerned with the following quasilinear Schrodinger system in R-N:
   {-epsilon(2)Delta u + V-1(x)u-epsilon(2)Delta(u(2))u = K-1(x)|u|22*(-2)u + h(1)(x,u,v)u,
   -epsilon(2)Delta v + V2(x)u-epsilon(2)Delta(v(2))v = K2(x)|v|22*(-2)v + h(2)(x,u,v)v,
   where N >= 3, V-i (x) is a nonnegative potential, K-i (x) is a bounded positive function, i = 1, 2. h(1) (x, u, v) u and h(2) (x, u, v) v are superlinear but subcritical functions. Under some proper conditions, minimax methods are employed to establish the existence of standing wave solutions for this system provided that epsilon is small enough, more precisely, for any m is an element of N, it has m pairs of solutions if epsilon is small enough. And these solutions (u(epsilon), v(epsilon)) -> (0, 0) in some Sobolev space as epsilon -> 0. Moreover, we establish the existence of positive solutions when epsilon = 1. The system studied here can model some interaction phenomena in plasma physics.