Ground state solutions for superlinear elliptic systems on RN

摘要

This paper is concerned with the existence of the ground state solutions for the following superlinear elliptic system of Hamiltonian type, {δu+V(x)u=g(x,v)inRN,-δv+V(x)v=f(x,u)inRN,u(x)→0andv(x)→0as{pipe}x{pipe}→~∞, where V∈C(RN,R) is periodic in x_1, x_2, .., x_N. We assume that 0 lies in a gap of the spectrum -δ+V, and f and g are both superlinear at 0 and infinity but they have different increasing rates at infinity. By proving all Cerami sequences for the energy functional are bounded, existence of a ground state solution is obtained.