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

Liao‎, F‎. ‎F‎. ‎; Tang, X‎. ‎H‎. ‎; Qin, D. D.

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

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