Existence of standing wave solutions for coupled quasilinear Schrödinger systems with critical exponents in RN.

This paper is concerned with the following quasilinear Schrödinger system in RN: {-ε2∆u + V1(x)u - ε2∆(u2)u = K1(x)∣u∣22*-2u + h1(x, u, v)u,-ε2∆v + V2(x)v - ε2∆(v2)v = K2(x)∣v∣22*-2v + h2(x, u, v)v, where N ≥ 3, Vi(x) is a nonnegative potential, Ki(x) is a bounded positive function, i = 1, 2. h1(x, u, v)u and h2(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 ε is small enough, more precisely, for any m ∊ N, it has m pairs of solutions if ε is small enough. And these solutions (uε, vε) → (0,0) in some Sobolev space as ε → 0. Moreover, we establish the existence of positive solutions when ε = 1. The system studied here can model some interaction phenomena in plasma physics. [ABSTRACT FROM AUTHOR]