数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 521-530.

• 论文 • 上一篇    下一篇

基于变分方法的奇异脉冲方程弱解的存在性

刘健1, 赵增勤2   

  1. 1 山东财经大学数学与数量经济学院 济南 250014;
    2 曲阜师范大学数学科学学院 山东曲阜 273165
  • 收稿日期:2015-09-27 修回日期:2016-04-02 出版日期:2016-06-26 发布日期:2016-06-26
  • 作者简介:刘健,kkword@126.com;赵增勤,zqzhaoy@163.com
  • 基金资助:

    国家自然科学基金(11571197)、山东省自然科学基金(ZR2012AQ024,ZR2014AM007)、山东财经大学杰出青年项目培育计划和高等学校博士学科点专项科研基金(20133705110003)资助

Variational Approach to Existence of Weak Solutions to Second-Order Singular Impulsive Problems

Liu Jian1, Zhao Zengqin2   

  1. 1 School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014;
    2 School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2015-09-27 Revised:2016-04-02 Online:2016-06-26 Published:2016-06-26
  • Supported by:

    Supported by the NSFC (11571197), the Shandong Provincial Natural Science Foundation (ZR2012AQ024, ZR2014AM007), the Project of Training Distinguished Young Scholars of SDUFE and the SRFDP (20133705110003)

摘要:

该文研究了一类具有扰动项的非线性奇异脉冲微分方程边值问题,利用变分方法结合临界点理论得到了弱解的存在性定理.

关键词: 变分方法, 奇异, 脉冲, 山路引理

Abstract:

In this paper, we consider the existence of weak solutions for a class of nonlinear singular impulsive boundary value problems with disturbance term. We obtain some new existence theorems of solutions by using variational methods combing with some critical-point theorems.

Key words: Variational method, Singular, Impulsive, Mountain pass theorem

中图分类号: 

  • O175.14