Multiple positive solutions for semilinear elliptic systems involving subcritical nonlinearities in R-N

In this paper, we investigate the effect of the coefficient f (x) of the subcritical nonlinearity. Under some assumptions, for sufficiently small epsilon, lambda, mu > 0, there are at least k (>= 1) positive solutions of the semilinear elliptic systems {-epsilon(2)Delta(u) over bar+(u) over bar = lambda g(x)vertical bar(u) over bar vertical bar(q-2)(u) over bar + alpha/alpha+beta f(x)vertical bar(u) over bar vertical bar(alpha-2)(u) over bar vertical bar(v) over bar vertical bar(beta) in R-N; -epsilon(2)Delta(u) over bar+<(vover bar> = mu h(x)vertical bar(v) over bar vertical bar(q-2)(v) over bar + beta/alpha+beta f(x)vertical bar(u) over bar vertical bar(alpha)(u) over bar vertical bar(v) over bar vertical bar(beta-2)(v) over bar in R-N; (u) over bar,(v) over bar is an element of H-1(R-N), where alpha > 1, beta > 1, 2 < q < p = alpha + beta < 2* = 2N/(N - 2) for N >= 3.