摘要
This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C(RN,R),V(x)is allowed to be sign-changing and inf Q>0,and F∈C1(R2,R)is superquadratic at both 0 and infinity but subcritical.Instead of the reduction approach used in Ding et al.(2014),we develop a more direct approach—non-Nehari manifold approach to obtain stronger conclusions but under weaker assumptions than those in Ding et al.(2014).We can find anε0>0 which is determined by terms of N,V,Q and F,and then we prove the existence of a ground state solution of Nehari-Pankov type to the coupled system for allε∈(0,ε0].
This paper is dedicated to studying the following elliptic system of Hamiltonian type:■where N≥3,V,Q∈C（RN,R）,V（x） is allowed to be sign-changing and inf Q>0,and F∈C1（R2,R）is superquadratic at both 0 and infinity but subcritical. Instead of the reduction approach used in Ding et al.（2014）,we develop a more direct approach—non-Nehari manifold approach to obtain stronger conclusions but under weaker assumptions than those in Ding et al.（2014）. We can find an ε0 > 0 which is determined by terms of N,V,Q and F,and then we prove the existence of a ground state solution of Nehari-Pankov type to the coupled system for all ε∈(0,ε0].
基金
supported by National Natural Science Foundation of China(Grant No.11171351)
