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Research Article | Open Access

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

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

Keywords

Dirichlet boundary value problemp-Laplacian differential equationsnon-instantaneous impulsevariational methodscritical point theory
CLC number: 34B37, 34K45, 58E30

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17269-17285
DOI: 10.3934/math.2022951

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Cite this article:
Yao W. Variational approach to non-instantaneous impulsive differential equations with p-Laplacian operator. AIMS Mathematics, 2022, 7(9): 17269-17285. https://doi.org/10.3934/math.2022951

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Received: 27 May 2022
Revised: 09 July 2022
Accepted: 18 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)