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论文类型：期刊论文

发表时间：2017-01-01

发表刊物：ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

收录刊物：ESI高被引论文、SCIE

期号：12

页面范围：1-23

ISSN号：1417-3875

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

摘要：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.