Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems View Full Text


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Article Info

DATE

2018-11-19

AUTHORS

Xianhua Tang, Xiaoyan Lin

ABSTRACT

This paper is dedicated to studying the following elliptic system of Hamiltonian type: {−ε2Δu+u+V(x)v=Q(x)Fv(u,v),x∈RN,−ε2Δv+v+V(x)u=Q(x)Fu(u,v),x∈RN,|u(x)|+|v(x)|→0,as|x|→∞ 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]. More... »

PAGES

1-22

References to SciGraph publications

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