摘要

In this article, we investigate how the coefficient f(z) affects the number of positive solutions of the quasilinear elliptic system
-Delta(p) u = lambda g(z)vertical bar u vertical bar(q-2)u + alpha/alpha + beta f(z)vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in Omega,
-Delta(p) v = mu h(z)vertical bar v vertical bar(q-2)v + beta/alpha + beta f(z)vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v in Omega,
u = v = 0 on partial derivative Omega,
where 0 is an element of Omega subset of R-N is a bounded domain, alpha > 1, beta > 1 and 1 < p < q < alpha + beta = p* = Np/N - p for N > 2p.