您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (8): 42-47.doi: 10.6040/j.issn.1671-9352.0.2023.062

•   • 上一篇    下一篇

非齐次Neumann边界条件下具有p-Laplacian算子的脉冲方程解的存在数量

杨国萍(),刘健*()   

  1. 山东财经大学统计与数学学院, 山东 济南 250014
  • 收稿日期:2023-02-14 出版日期:2024-08-20 发布日期:2024-07-31
  • 通讯作者: 刘健 E-mail:yangguoping9@163.com;liujianmath@163.com
  • 作者简介:杨国萍(1979— ), 女, 讲师, 硕士, 研究方向为变分方法. E-mail: yangguoping9@163.com
  • 基金资助:
    山东省自然科学基金资助项目(ZR2021MA070)

Existence number of solutions for impulsive equations involving p-Laplacian operator with nonhomogeneous Neumann boundary conditions

Guoping YANG(),Jian LIU*()   

  1. School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
  • Received:2023-02-14 Online:2024-08-20 Published:2024-07-31
  • Contact: Jian LIU E-mail:yangguoping9@163.com;liujianmath@163.com

摘要:

在非齐次Neumann边界条件下研究一类具有p-Laplacian算子的脉冲微分方程非平凡解的存在性的充分条件, 在非线性项满足L1-Carathéodory条件下利用变分方法结合相应的临界点理论得到非平凡解的存在数量的2个定理, 给出具体的例子, 结合牛顿迭代法来阐明本文所得到的结论。

关键词: p-Laplacian算子, 非齐次边界条件, 脉冲项

Abstract:

The sufficient condition of the existence of nontrivial solutions for some p-Laplacian impulsive differential equations with nonhomogeneous Neumann boundary conditions is obtained. We get two theorems on the numbers of nontrivial solutions via variational methods and corresponding critical points theory when nonlinear terms satisfying the L1-Carathéodory condition and applying the Newton-iterative method into concrete examples to illustrate the obtained conclusions.

Key words: p-Laplacian operator, nonhomogeneous boundary condition, impulsive effect

中图分类号: 

  • O175.2
1 BONANNO G , IANNIZZOTTO A , MARRAS M . Two positive solutions for superlinear Neumann problems with a complete Sturm-Liouville operator[J]. Journal of Convex Analysis, 2018, 25 (2): 421- 434.
2 D'AGU G , SCIAMMETTA A , TORNATORE E . Two non-zero solutions for Sturm-Liouville equations with mixed boundary conditions[J]. Nonlinear Analysis: Real World Applications, 2019, 47, 324- 331.
doi: 10.1016/j.nonrwa.2018.11.002
3 LIU Jian , YU Wenguang . Two solutions to superlinear Hamiltonian systems with impulsive effects[J]. Applied Mathematics Letters, 2020, 102, 106162.
doi: 10.1016/j.aml.2019.106162
4 BONANNO G , CANDITO P . Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities[J]. Journal of Differential Equations, 2008, 244 (12): 3031- 3059.
doi: 10.1016/j.jde.2008.02.025
5 BONANNO G , LIVREA R . Multiple periodic solutions for Hamiltonian systems with not coercive potential[J]. Journal of Mathematical Analysis and Applications, 2010, 363 (2): 627- 638.
doi: 10.1016/j.jmaa.2009.09.025
6 LIU Jian , ZHAO Zengqin , ZHANG Tongqian . Multiple solutions to damped Hamiltonian systems with impulsive effects[J]. Applied Mathematics Letters, 2019, 91, 173- 180.
doi: 10.1016/j.aml.2018.12.013
7 LIU Jian , ZHAO Zengqin . Multiple solutions for impulsive problems with non-autonomous perturbations[J]. Applied Mathematics Letters, 2017, 64, 143- 149.
doi: 10.1016/j.aml.2016.08.020
8 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, 2016, 59 (5): 609- 622.
LIU Jian , ZHAO Zengqin . Existence of classical solutions to impulsive boundary value problems under Cerami condition[J]. Acta Mathematica Sinica: Chinese Series, 2016, 59 (5): 609- 622.
9 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, 2019, 62 (3): 441- 448.
doi: 10.3969/j.issn.0583-1431.2019.03.009
LIU Jian , ZHAO Zengqin , YU Wenguang . The existence of triple classical solutions to impulsive problems with small non-autonomous perturbations[J]. Acta Mathematica Sinica: Chinese Series, 2019, 62 (3): 441- 448.
doi: 10.3969/j.issn.0583-1431.2019.03.009
10 刘健, 赵增勤. 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.
LIU Jian , ZHAO Zengqin . The numbers of nontrivial weak solutions to fourth-order impulsive elastic beam equations[J]. Acta Mathematica Sinica: Series A, 2021, 64 (1): 99- 106.
11 NIETO J , O'REGAN D . Variational approach to impulsive differential equations[J]. Nonlinear Analysis, 2009, 10, 680- 690.
12 NIETO J . Variational formulation of a damped Dirichlet impulsive problem[J]. Applied Mathematics Letters, 2010, 23, 940- 942.
doi: 10.1016/j.aml.2010.04.015
13 SUN Juntao , CHEN Haibo , YANG Liu . Variational methods to fourth-order impulsive differential equations[J]. Journal of Applied Mathematics and Computing, 2011, 35, 323- 340.
doi: 10.1007/s12190-009-0359-x
14 BONANNO G . Relations between the mountain pass theorem and local minima[J]. Advances in Nonlinear Analysis, 2012, 1 (3): 205- 220.
15 BONANNO G , D'AGU G . Two non-zero solutions for elliptic Dirichlet problems[J]. Zeitschrift für Analysis und ihre Anwendungen, 2016, 35 (4): 449- 464.
doi: 10.4171/zaa/1573
16 MAWHIN J , WILLEM M . Critical point theory and hamiltonian systems[M]. Berlin: Springer-Verlag, 1989.
17 LI Wei , WANG Yanhui . Three solutions for a class of gradient mixed boundary value systems depending on two parameters[J]. Annals of Applied Mathematics, 2015, 31 (4): 411- 422.
[1] 仲秋艳,张兴秋. 含参数及p-Laplacian算子的奇异分数阶微分方程积分边值问题的正解[J]. 山东大学学报(理学版), 2016, 51(6): 78-84.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 邹国平1,马儒宁1,丁军娣2,钟宝江3. 基于显著性加权颜色和纹理的图像检索[J]. J4, 2010, 45(7): 81 -85 .
[2] 陈 莉 . 不确定奇异系统的鲁棒故障诊断滤波器设计[J]. J4, 2007, 42(7): 62 -65 .
[3] 孟祥波1,张立东1,杜子平2. 均值-方差标准下带跳的保险公司投资与再保险策略[J]. 山东大学学报(理学版), 2014, 49(05): 36 -40 .
[4] 彭振华,徐义红*,涂相求. 近似拟不变凸集值优化问题弱有效元的最优性条件[J]. 山东大学学报(理学版), 2014, 49(05): 41 -44 .
[5] 袁晖坪 . 行(列)对称矩阵的Schur分解和正规阵分解[J]. J4, 2007, 42(10): 123 -126 .
[6] 郭兰兰1,2,耿介1,石硕1,3,苑飞1,雷丽1,杜广生1*. 基于UDF方法的阀门变速关闭过程中的#br# 水击压强计算研究[J]. 山东大学学报(理学版), 2014, 49(03): 27 -30 .
[7] 史开泉. 信息规律智能融合与软信息图像智能生成[J]. 山东大学学报(理学版), 2014, 49(04): 1 -17 .
[8] 章 玲,周德群 . λ模糊测度及其Mbius变换和关联系数间关系的推导[J]. J4, 2007, 42(7): 33 -37 .
[9] 吴大千,杜 宁,王 炜,翟 雯,王玉芳,王仁卿,张治国* . 昆嵛山森林群落下灌草层结构与多样性研究[J]. J4, 2007, 42(1): 83 -88 .
[10] 孙 蕾,顾春丽,房用,刘昌兰,王家福,曲永赟 . 赤松和黑松花粉的营养成分测定及功能分析[J]. J4, 2006, 41(1): 130 -132 .