Ground state solution of a noncooperative elliptic system

Cyril Joel Batkam

Published 2012-10-30, updated 2013-08-30Version 2

In this paper, we study the existence of a ground state solution, that is, a non trivial solution with least energy, of a noncooperative semilinear elliptic system on a bounded domain. By using the method of the generalized Nehari manifold developed recently by Szulkin and Weth, we prove the existence of a ground state solution when the nonlinearity is subcritical and satisfies a weak superquadratic condition.