Abstract
Let Omega be a bounded domain in R-n (n >= 2) with a smooth boundary partial derivative Omega. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system
-Delta u = a(1)(x)u(alpha)v(r) in Omega, u vertical bar(partial derivative Omega) = 0,
-Delta u = a(2)(x)v(beta)u(s) in Omega, u vertical bar(partial derivative Omega) = 0,
Here r, s is an element of R, alpha, beta < 1 such that gamma := (1 - alpha)(1 - beta) - rs > 0 and the functions a(i) (i = 1, 2) are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.