UNIQUENESS OF POSITIVE SOLUTIONS FOR A CLASS OF SCHRODINGER SYSTEMS WITH SATURABLE NONLINEARITY

This paper is devoted to the study of the nonexistence and the uniqueness of positive solutions for a class of the following nonlinear coupled Schrodinger systems with saturable nonlinearity { -Delta u(1) + lambda(1)u(1) = u(1)(mu(1)u(1)(2) + beta u(2)(2)) / 1 + s(mu(1)u(1)(2) + beta u(2)(2)) in R-N, -Delta u(2) + lambda(2)u(2) = u(2)(mu(2)u(2)(2) + beta u(1)(2)) / 1 + s(mu(2)u(2)(2) + beta u(1)(2)) in R-N, u(1), u(2) is an element of H-1 (R-N), u(1) > 0, u(2) > 0 in R-N, where lambda(j), mu(j), j = 1,2, are positive constants, s is a positive parameter and beta is a positive coupling parameter. Moreover, we will show that any positive solution is a priori bounded.