Variational approach to non-instantaneous impulsive differential equations with $ p $-Laplacian operator

Wangjin Yao; Wangjin Yao

doi:10.3934/math.2022951

AIMS Mathematics

2022, Volume 7, Issue 9: 17269-17285. doi: 10.3934/math.2022951

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Research article

Variational approach to non-instantaneous impulsive differential equations with $ p $-Laplacian operator

Wangjin Yao ^,

Key Laboratory of Applied Mathematics of Fujian Province University, School of Mathematics and Finance, Putian University, Putian 351100, China

Received: 27 May 2022 Revised: 09 July 2022 Accepted: 18 July 2022 Published: 25 July 2022
MSC : 34B37, 34K45, 58E30

In this paper, we consider the existence, multiplicity and nonexistence of solutions for a class of $ p $-Laplacian differential equations with non-instantaneous impulses. By using variational methods and critical point theory, we obtain that the impulsive problem has at least one nontrivial solution, at least two nontrivial solutions and no nontrivial solution.
- Dirichlet boundary value problem,
- $ p $-Laplacian differential equations,
- non-instantaneous impulse,
- variational methods,
- critical point theory
Citation: Wangjin Yao. Variational approach to non-instantaneous impulsive differential equations with $ p $-Laplacian operator[J]. AIMS Mathematics, 2022, 7(9): 17269-17285. doi: 10.3934/math.2022951

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Abstract

In this paper, we consider the existence, multiplicity and nonexistence of solutions for a class of $ p $-Laplacian differential equations with non-instantaneous impulses. By using variational methods and critical point theory, we obtain that the impulsive problem has at least one nontrivial solution, at least two nontrivial solutions and no nontrivial solution.

References

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