Ground state solution of a noncooperative elliptic system

TL;DR

This paper proves the existence of a least-energy nontrivial solution for a noncooperative elliptic system on bounded domains using the generalized Nehari manifold method, under subcritical and weak superquadratic conditions.

Contribution

It introduces the application of the generalized Nehari manifold method to establish ground state solutions for noncooperative elliptic systems.

Findings

Existence of ground state solutions under specified conditions

Application of generalized Nehari manifold method to noncooperative systems

Solution characterized by least energy among nontrivial solutions

Abstract

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.