ON VECTOR SOLUTIONS FOR COUPLED NONLINEAR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTS

Abstract

In this paper, we study the existence and asymptotic behavior of a solution with positive components (which we call a vector solution) for the coupled system of nonlinear Schrodinger equations with doubly critical exponents [GRAPHICS] u, v > 0 in Omega, u, v = 0 on partial derivative Omega as the coupling coefficient beta is an element of R tends to 0 or +infinity, where the domain Omega subset of R-N (N >= 3) is smooth bounded and certain conditions on lambda 1, lambda 2 > 0 and mu 1, mu 2 > 0 are imposed. This system naturally arises as a counterpart of the Brezis-Nirenberg problem (Comm. Pure Appl. Math. 36: 437-477, 1983).