基于变分方法的脉冲微分方程 Neumann 边值问题多重解的存在性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 447-457.

基于变分方法的脉冲微分方程 Neumann 边值问题多重解的存在性

廖丹^1,²,张慧萍³,姚旺进^1,^2,^*()

¹应用数学福建省高校重点实验室福建莆田 351100
²莆田学院数学与金融学院福建莆田 351100
³福建师范大学数学与统计学院福州 350007

收稿日期:2021-08-27 修回日期:2022-09-20 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 姚旺进，E-mail： 13635262963@163.com
基金资助:
福建省自然科学基金(2021J05237);福建省高校创新团队培育计划(2018-39)

Variational Approach to Existence of Multiple Solutions for Neumann Boundary Value Problem of Impulsive Differential Equations

Liao Dan^1,²,Zhang Huiping³,Yao Wangjin^1,^2,^*()

¹Key Laboratory of Applied Mathematics of Fujian Province University, Fujian Putian 351100
²School of Mathematics and Finance, Putian University, Fujian Putian 351100
³College of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007

Received:2021-08-27 Revised:2022-09-20 Online:2023-04-26 Published:2023-04-17
Supported by:
Natural Science Foundation of Fujian Province(2021J05237);Program for Innovative Research Team in Science and Technology in Fujian Province University(2018-39)

摘要/Abstract

摘要：

该文研究一类含有$p$-Laplacian 算子的脉冲微分方程 Neumann 边值问题解的多重性. 当非线性项不满足Ambrosetti-Rabinowitz 条件时, 通过变分方法获得该脉冲边值问题具有无穷多个古典解.

关键词: Neumann 边值问题, Cerami 条件, 变分方法

Abstract:

In this paper, we consider the multiplicity of solutions for Neumann boundary value problem of impulsive differential matrixs with $p$-Laplacian operator. Under the assumption that the nonlinearity does not satisfy Ambrosetti-Rabinowitz condition, infinitely many classical solutions for the impulsive boundary value problem are obtained via variational method.

Key words: Neumann boundary value problem, Cerami condition, Variational method

中图分类号:

O175.14

廖丹, 张慧萍, 姚旺进. 基于变分方法的脉冲微分方程 Neumann 边值问题多重解的存在性[J]. 数学物理学报, 2023, 43(2): 447-457.

Liao Dan, Zhang Huiping, Yao Wangjin. Variational Approach to Existence of Multiple Solutions for Neumann Boundary Value Problem of Impulsive Differential Equations[J]. Acta mathematica scientia,Series A, 2023, 43(2): 447-457.

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