具有无界势能的 Kirchhoff-型差分方程多个同宿轨的存在性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 80-92.

具有无界势能的 Kirchhoff-型差分方程多个同宿轨的存在性

王振国^1,^*(),丁廉业²

1.太原学院数学系太原 030032
2.黄淮学院数学与统计学院河南驻马店 463000

收稿日期:2022-10-26 修回日期:2023-08-28 出版日期:2024-02-26 发布日期:2024-01-10
通讯作者: 王振国, E-mail：wangzhg123@163.com
基金资助:
国家自然科学基金(11971126);太原学院科研项目(23TYYB04)

Multiple Homoclinic Solutions for the Kirchhoff-type Difference Equations with Unbounded Potential

Wang Zhenguo^1,^*(),Ding Lianye²

1. Department of Mathematics, Taiyuan University, Taiyuan 030032
2. School of Mathematics and Statistics, Huanghuai University, Henan Zhumadian 463000

Received:2022-10-26 Revised:2023-08-28 Online:2024-02-26 Published:2024-01-10
Supported by:
NSFC(11971126);Scientific Research Project of Taiyuan University(23TYYB04)

摘要/Abstract

摘要：

该文运用临界点理论研究了具有无界势能的 Kirchhoff-型差分方程多个同宿轨的存在性. 特别地, 文中借助于非线性项次线性增长条件和一些技巧证明了能量泛函满足 Palais-Smale 紧性条件. 最后举例说明主要结论.

关键词: Kirchhoff-型差分方程, Palais-Smale 序列, 临界点理论, 同宿轨

Abstract:

In this paper, we study the existence of multiple homoclinic solutions for the Kirchhoff-type difference equations with unbounded potential by using critical point theory. In our work, the nonlinearity is allowed to grow sublinearly, and some technical methods are used to verify the energy functional satisfying the Palais-Smale conditions. Finally, one example is given to illustrate our main results.

Key words: Kirchhoff-type difference equations, Palais-Smale sequence, Critical point theory, Homoclinic solutions

中图分类号:

O175.8

王振国, 丁廉业. 具有无界势能的 Kirchhoff-型差分方程多个同宿轨的存在性[J]. 数学物理学报, 2024, 44(1): 80-92.

Wang Zhenguo, Ding Lianye. Multiple Homoclinic Solutions for the Kirchhoff-type Difference Equations with Unbounded Potential[J]. Acta mathematica scientia,Series A, 2024, 44(1): 80-92.

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