四阶脉冲弹性梁方程非平凡弱解的存在数量被引量：2

The Numbers of Nontrivial Weak Solutions to Fourth-order Impulsive Elastic Beam Equations

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摘要本文研究了一类具有脉冲项的四阶弹性梁微分方程边值问题,在非线性项不连续的情况下利用变分方法结合相应的临界点定理得到了非平凡弱解的存在数量,最后给出具体的例子,结合牛顿迭代法来验证所得到的结论. In this paper,the numbers of nontrivial solutions to super linear fourthorder impulsive elastic beam equations are obtained.We get two theorems via variational methods and corresponding two-critical-points theorems.Combining with the Newton-iterative method,two examples are presented to illustrate the value of the obtained theorems.

作者刘健赵增勤于文广 Jian LIU;Zeng Qin ZHAO;Wen Guang YU(School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics,JVnan 250014,P.R.China;School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China;School of Insurance,Shandong University of Finance and Economics,JVnan 250014,P.R.China)

机构地区山东财经大学数学与数量经济学院曲阜师范大学数学科学学院山东财经大学保险学院

出处《数学学报（中文版）》 CSCD 北大核心 2021年第1期99-106,共8页 Acta Mathematica Sinica：Chinese Series

基金国家自然科学基金(11571197,11601269) 教育部人文社会科学研究项目(16YJC630070) 山东省自然科学基金(ZR2017MA048,ZR2018MG002) 山东财经大学青年优秀人才支持计划山东省高等学校优势学科人才团队培育计划(1716009) 泰山学者工程专项经费(tsqn20161041)。

关键词弹性梁方程脉冲变分方法 elastic beam equations impulsive effects variational methods

分类号 O175.14 [理学—基础数学]

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参考文献2

1刘健,赵增勤.Cerami条件下脉冲边值问题古典解的存在性[J].数学学报（中文版）,2016,59(5):609-622. 被引量：5
2刘健,赵增勤,于文广.具非自治微小扰动的脉冲方程三个古典解的存在性[J].数学学报（中文版）,2019,62(3):441-448. 被引量：5

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