# New conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms

Document Type: Research Paper

Authors

1 School of Mathematics and Statistics Central South University Changsha‎, ‎410083‎, ‎Hunan newline Department of Mathematics‎, ‎Xiangnan University‎, ‎Chenzhou‎, ‎423000‎, ‎Hunan‎, ‎P.R‎. ‎China

2 School of Mathematics and Statistics Central South University Changsha‎, ‎410083‎, ‎Hunan‎, ‎P.R‎. ‎China

3 School of Mathematics and Statistics Central South University Changsha‎, ‎410083‎, ‎Hunan‎, ‎P.R‎. ‎China

Abstract

This paper is concerned with the following elliptic system:
$$left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right.$$
for $x in {R}^{N}$, where $V$, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and establish the existence of ground state solutions with mild assumptions on $f$ and $g$.

Keywords

Main Subjects

### History

• Receive Date: 18 July 2013
• Revise Date: 15 July 2014
• Accept Date: 15 July 2014