Infinitely many solutions for linearly coupled Schrodinger systems in R3

In this paper, we consider the following linearly coupled nonlinear Schrodinger system: { -Delta u + P(|y|)u = u(3) +lambda(|y|)v in R-3, -Delta v + Q(|y|)v = v(3) + lambda(|y|)u in R-3, (A) u, v is an element of H-1(R-3), where P(|y|), Q(|y|), and lambda(|y|) are radial, positive, and continuous and satisfying that lim(|y|->infinity) P(|y|) = lim(|y|->infinity) Q(|y|) = 1, lim(|y|->infinity) lambda(|y|) = lambda is an element of(0, 1). When lambda(|y|) < min{P(|y|), Q(|y|)} and P(|y|), Q(|y|), lambda(|y|) satisfy some weak power decay condition at infinity; we show that problem (.) has infinitelymany nonradial positive solutions by using the Lyapunov-Schmidt reduction method.