$\mathbf{R}^3$上具有一般凹凸非线性项的Klein-Gordon-Born-Infeld方程无穷多解的存在性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 637-649.

$\mathbf{R}^3$ 上具有一般凹凸非线性项的Klein-Gordon-Born-Infeld方程无穷多解的存在性

陈尚杰^1,²()

1.重庆工商大学数学与统计学院重庆 400067
2.经济社会应用统计重庆市重点实验重庆 400067

收稿日期:2023-04-24 修回日期:2023-09-27 出版日期:2024-06-26 发布日期:2024-05-17
作者简介:陈尚杰, Email:11183356@qq.com
基金资助:
重庆市研究生导师团队建设项目(yds223010);重庆工商大学统计测度和应用团队(ZDPTTD201909)

Infinitely Many Large Energy Solutions for the Klein-Gordon-Born-Infeld Equation on $\mathbf{R}^3$ with Concave and Convex Nonlinearities

Chen Shangjie^1,²()

1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067

Received:2023-04-24 Revised:2023-09-27 Online:2024-06-26 Published:2024-05-17
Supported by:
Team Building Project for Graduate Tutors in Chongqing(yds223010);CTBU Statistics Measure and Applications Group(ZDPTTD201909)

摘要/Abstract

摘要：

该文运用临界点理论中的 $\mathbf{Z}_2$ -山路定理得到了 $\mathbf{R}^3$ 上具有凹凸非线性项的 Klein-Gordon 方程和 Born-Infeld 理论耦合系统无穷多解的存在性.

关键词: Klein-Gordon 方程, Born-Infeld 理论, 变分方法, $\mathbf{Z}_2$ -山路定理

Abstract:

In this paper, we obtained the existence of infinitely many large energy solutions for the Klein-Gordon equation with concave and convex nonlinearities coupled with Born-Infeld theory on $\mathbb{R}^3$ by using $\mathbf{Z}_2$ -Mountain Pass Theorem in critical point theory.

Key words: Klein-Gordon equation, Born-Infeld theory, Variational methods, $\mathbf{Z}_2$ -Mountain Pass Theorem

中图分类号:

O176.3

陈尚杰. $\mathbf{R}^3$ 上具有一般凹凸非线性项的Klein-Gordon-Born-Infeld方程无穷多解的存在性[J]. 数学物理学报, 2024, 44(3): 637-649.

Chen Shangjie. Infinitely Many Large Energy Solutions for the Klein-Gordon-Born-Infeld Equation on $\mathbf{R}^3$ with Concave and Convex Nonlinearities[J]. Acta mathematica scientia,Series A, 2024, 44(3): 637-649.

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