Abstract
In this article, we study the existence and the asymptotic behavior of positive continuous solutions for the following elliptic coupled system
{-Delta u = p(x)u(alpha)v(a) in D,
-Delta u = p(x)u(b)v(beta) in D,
u(/partial derivative D) = v(/partial derivative D) = 0,
lim(vertical bar x vertical bar ->infinity )u(x) = lim(vertical bar x vertical bar ->infinity) v(x) = 0,
where D is an unbounded regular domain in R-n, n >= 3, with a compact boundary. The exponents alpha, beta is an element of ( 1. 1). a, b is an element of R such that (1 -vertical bar alpha vertical bar)(1-vertical bar beta vertical bar) - vertical bar ab vertical bar > 0 and p, q are positive continuous functions on D satisfying some suitable assumptions with reference to Karamata regular variation theory.