Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity

Abstract

This article concerns the Hamiltonian elliptic system: ⎧ ⎪ ⎨ ⎪ ⎩-ϕ + V(x)ϕ = G ψ (x, ϕ, ψ) inR N ,-ψ + V(x)ψ = G ϕ (x, ϕ, ψ) in R N , ϕ, ψ ∈ H 1 (R N). Assuming that the potential V is periodic and 0 lies in a spectral gap of σ (-+ V), least energy solution of the system is obtained for the super-quadratic case with a new technical condition, and the existence of ground state solutions of Nehari-Pankov type is established for the asymptotically quadratic case. The results obtained in the paper generalize and improve related ones in the literature.

Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schrödinger System

“…Other methods have been applied such as Darboux transformation, least energy solutions, Fokas method, Morse index, etc. The readers may refer to [3][4][5][6][7][8][9][10][11][12][13][14][15]).…”