Ground state solutions to some Indefinite Nonlinear Schrödinger equations on lattice graphs

2023/02/28 by Wendi Xu, Xu, Wendi
Mathematics · Physics and Astronomy · #35Q55 #39A14 #58E30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2302.14608

openalex publication_date 2023/02/28 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Schrödinger type equation -Δu+V(x)u=f(x,u) on the lattice graph ℤ^N with indefinite variational functional, where -Δ is the discrete Laplacian. Specifically, we assume that V(x) and f(x,u) are periodic in x, f satisfies some growth condition and 0 lies in a spectral gap of (-Δ+ V). We obtain ground state solutions by using the method of generalized Nehari manifold which has been introduced in arXiv:1801.06872.

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