四阶脉冲弹性梁方程非平凡弱解的存在数量

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四阶脉冲弹性梁方程非平凡弱解的存在数量刘健¹, 赵增勤², 于文广³1 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曲阜 273165;
3 山东财经大学保险学院济南 250014 The Numbers of Nontrivial Weak Solutions to Fourth-order Impulsive Elastic Beam Equations Jian LIU¹, Zeng Qin ZHAO², Wen Guang YU³1 School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Ji'nan 250014, P. R. China;
2 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China;
3 School of Insurance, Shandong University of Finance and Economics, Ji'nan 250014, P. R. China

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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.

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收稿日期: 2019-11-18

MR (2010):

O175.14

基金资助: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****工程专项经费（tsqn20161041）

作者简介: 刘健,E-mail:liujianmath@163.com;赵增勤,E-mail:zqzhaoy@163.com;于文广,E-mail:yuwg@sdufe.edu.cn

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刘健, 赵增勤, 于文广. 四阶脉冲弹性梁方程非平凡弱解的存在数量[J]. 数学学报, 2021, 64(1): 99-106. Jian LIU, Zeng Qin ZHAO, Wen Guang YU. The Numbers of Nontrivial Weak Solutions to Fourth-order Impulsive Elastic Beam Equations. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 99-106.

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