JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 42-47.doi: 10.6040/j.issn.1671-9352.0.2023.062

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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

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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

CLC Number: 

  • 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.
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