MULTIPLE SOLUTIONS FOR $ P $-LAPLACIAN KIRCHHOFF-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES

Wangjin Yao; Huiping Zhang

doi:10.11948/20240118

2025 Volume 15 Issue 1

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Wangjin Yao, Huiping Zhang. MULTIPLE SOLUTIONS FOR $ P $-LAPLACIAN KIRCHHOFF-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 422-441. doi: 10.11948/20240118

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Wangjin Yao, Huiping Zhang. MULTIPLE SOLUTIONS FOR $ P $-LAPLACIAN KIRCHHOFF-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 422-441. doi: 10.11948/20240118

MULTIPLE SOLUTIONS FOR $ P $-LAPLACIAN KIRCHHOFF-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES

Wangjin Yao^1,,
Huiping Zhang^2, ,

1.
Fujian Key Laboratory of Financial Information Processing, Putian University, Putian 351100, China
2.
School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China

Author Bio: Email: 13635262963@163.com(W. Yao)
Corresponding author: Email: zhanghpmath@163.com(H. Zhang)
Fund Project: The authors were supported by Natural Science Foundation of Fujian Province (Grant Nos. 2023J01994, 2023J01995, 2021J05237), Program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. 2018–39), Education and Research Project for Middle and Young Teachers in Fujian Province (Grant No. JAT231093) and Mathematics Discipline Alliance Project in Fujian Province University (Grant No. 2024SXLMMS05)

Abstract

Abstract

In this paper, we consider a class of $ p $-Laplacian Kirchhoff-type fractional differential equations with instantaneous and non-instantaneous impulses. The existence of at least two distinct weak solutions and infinitely many weak solutions is obtained based on variational methods.
- Fractional differential equations /
- Kirchhoff-type /
- variational methods /
- instantaneous impulse /
- non-instantaneous impulse
MSC: 26A33, 34A08, 34B15, 34B37, 58E30

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References

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