Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms

Guanwei Chen; Martin Schechter

doi:10.3934/dcdsb.2021124

Article Contents

2022, Volume 27, Issue 4: 2107-2114. Doi: 10.3934/dcdsb.2021124

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Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms

Guanwei Chen^1, , and
Martin Schechter^2,

1.
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China
2.
Department of Mathematics, University of California, Irvine, CA 92697-3875, USA

^* Corresponding author: Guanwei Chen
^* Corresponding author: Guanwei Chen

Received: September 30, 2020

Revised: February 28, 2021

Early access: April 2021

Published: April 2022

This work is supported by National Natural Science Foundation of China (No. 11771182)

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Abstract

In infinite $ m $-dimensional lattices, we obtain the existence of two nontrivial solutions for a class of non-periodic Schrödinger lattice systems with perturbed terms, where the potentials are coercive and the nonlinearities are asymptotically linear at infinity. In addition, examples are given to illustrate our results.

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Mathematics Subject Classification: Primary: 35Q51, 35Q55, 39A12; Secondary: 39A70.

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