Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 49, pp. 1-8.

Title: Existence of least energy solutions to  coupled elliptic systems
       with critical nonlinearities
 
Authors: Gong-Ming Wei (Univ. of Shanghai for Science and Tech., China)
         Yan-Hua Wang  (Shanghai Univ. of Finance and Economics, China)

Abstract: 
 In this paper we study  the existence of  nontrivial solutions of
 elliptic systems with critical nonlinearities and subcritical
 nonlinear coupling interactions, under  Dirichlet or Neumann
 boundary conditions. These equations are motivated from solitary
 waves of nonlinear Schrodinger systems in physics.  Using minimax
 theorem and by estimates on  the least energy, we prove the
 existence of nonstandard least energy solutions, i.e. solutions with
 least energy and  each component is nontrivial.
 
Submitted October 18, 2007. Published April 04, 2008.
Math Subject Classifications: 35B33, 35J50.
Key Words: Least energy solutions; Nehari manifold;
           critical exponent; coupled elliptic systems.