Homoclinic solutions for a difference equation with the mean curvature operator and periodic coefficients

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-01 DOI:10.1016/j.aml.2025.109737

Xiaoguang Li , Zhan Zhou

引用次数: 0

Abstract

We establish the existence of nontrivial homoclinic solutions for a class of difference equation with the mean curvature operator and periodic potentials via variational methods. Specifically, a novel approach inspired by the vanishing in the concentration–compactness principle is employed to prove the boundedness of Cerami sequences. Finally, we investigate the strict monotonicity and sign-definiteness of the obtained homoclinic solution, which have rarely been discussed.

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具有平均曲率算子和周期系数的差分方程的同斜解

利用变分方法，建立了一类具有平均曲率算子和周期势的差分方程非平凡同斜解的存在性。具体来说，利用浓度-紧致原理中的消失原理来证明陶瓷序列的有界性。最后，我们研究了所得到的同斜解的严格单调性和符号确定性，这是以往很少讨论的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.