Variational approach to <i>p</i>-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses

Zhilin Li; Guoping Chen; Weiwei Long; Xinyuan Pan; Zhilin Li; Guoping Chen; Weiwei Long; Xinyuan Pan

doi:10.3934/math.2022933

AIMS Mathematics

2022, Volume 7, Issue 9: 16986-17000. doi: 10.3934/math.2022933

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Research article

Variational approach to p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses

1.
College of Mathematics and Statistics, Jishou University, Jishou, Hunan, China
2.
School of Civil Engineering and Architecture, Jishou University, Jishou, Hunan, China

Received: 10 April 2022 Revised: 16 June 2022 Accepted: 20 June 2022 Published: 19 July 2022
MSC : 34A08, 34B37

In this paper, we examine the existence of solutions of p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses. New criteria guaranteeing the existence of infinitely many solutions are established for the considered problem. The problem is reduced to an equivalent form such that the weak solutions of the problem are defined as the critical points of an energy functional. The main result of the present work is established by using a variational approach and a mountain pass lemma. Finally, an example is given to illustrate our main result.
- fractional differential equation,
- impulsive effects,
- p-Laplacian operator,
- variational approach,
- mountain pass lemma
Citation: Zhilin Li, Guoping Chen, Weiwei Long, Xinyuan Pan. Variational approach to p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses[J]. AIMS Mathematics, 2022, 7(9): 16986-17000. doi: 10.3934/math.2022933

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Abstract

In this paper, we examine the existence of solutions of p-Laplacian fractional differential equations with instantaneous and non-instantaneous impulses. New criteria guaranteeing the existence of infinitely many solutions are established for the considered problem. The problem is reduced to an equivalent form such that the weak solutions of the problem are defined as the critical points of an energy functional. The main result of the present work is established by using a variational approach and a mountain pass lemma. Finally, an example is given to illustrate our main result.

References

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