Ground state solutions to some Indefinite Nonlinear Schr\"{o}dinger equations on lattice graphs

Author name not available (Why is that?)

Publication date: 28 February 2023

Abstract: In this paper, we consider the Schr"odinger type equation

- D e l t a u + V (x) u = f (x, u)

on the lattice graph

m a t h b b Z^{N}

with indefinite variational functional, where

- D e l t a

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

(- D e l t a + 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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