EXISTENCE AND EXPONENTIAL STABILITY FOR A NEW CLASS OF FIRST-ORDER IMPULSIVE EVOLUTION EQUATIONS

Caijing Jiang; Fengzhen Long

doi:10.11948/20240477

2025 Volume 15 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(6): 3535-3556

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Caijing Jiang, Fengzhen Long. EXISTENCE AND EXPONENTIAL STABILITY FOR A NEW CLASS OF FIRST-ORDER IMPULSIVE EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3535-3556. doi: 10.11948/20240477

Citation:

Caijing Jiang, Fengzhen Long. EXISTENCE AND EXPONENTIAL STABILITY FOR A NEW CLASS OF FIRST-ORDER IMPULSIVE EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(6): 3535-3556. doi: 10.11948/20240477

EXISTENCE AND EXPONENTIAL STABILITY FOR A NEW CLASS OF FIRST-ORDER IMPULSIVE EVOLUTION EQUATIONS

Caijing Jiang^1, ,,
Fengzhen Long^2,

1.
Institute for History and Culture of Science, Guangxi Minzu University, Nanning 530006, Guangxi Province, China
2.
School of Mathematical Sciences, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, Guangxi Province, China

Author Bio: Email: fengzhen_long@126.com(F. Long)
Corresponding author: Email: caijing_jiang@163.com(C. Jiang)
Fund Project: The first author is supported by the Basic Ability Improvement Project for Middle-Aged and Young Teachers of Universities in Guangxi (No. 2022KY1210). The second author is supported by the Guangxi Natural Science Foundation (2025GXNSFBA069518), the Scientific Research Project of Guangxi Minzu University (2022KJQD07) and the Basic Ability Improvement Project for Middle-Aged and Young Teachers of Universities in Guangxi (2024KY0183)

Abstract

Abstract

The aim of this paper is to present systematic methods for analyzing the existence and the exponential stability of a new class of first-order impulsive evolution equations. We initially provide two existence results of mild solutions for the equations using two kinds of methods. Subsequently, we also explore the exponential stability of the equation. Lastly, we present some applications in differential hemivariational inequalities to demonstrate our main results.
- Impulsive delay evolution equation /
- mild solution /
- existence /
- exponential stability
MSC: 34A12, 34B37, 34K20

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