Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems.

This paper is dedicated to studying the following elliptic system of Hamiltonian type: { − ε 2 Δ u + u + V (x) v = Q (x) F v (u , v) , x ∈ R N , − ε 2 Δ v + v + V (x) u = Q (x) F u (u , v) , x ∈ R N , | u (x) | + | v (x) | → 0 , a s | x | → ∞ where N ⩾ 3, V, Q ∈ C (R N , R) , V (x) is allowed to be sign-changing and inf Q > 0, and F ∈ C 1 (R 2 , 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]. [ABSTRACT FROM AUTHOR]