WELL-POSEDNESS OF NONLOCAL IMPULSIVE PROBLEMS OF NON-AUTONOMOUS EVOLUTION EQUATIONS WITH DELAY

Huanhuan Wang; Xiaoya Liu; Xuping Zhang

doi:10.11948/20250196

2026 Volume 16 Issue 2

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Huanhuan Wang, Xiaoya Liu, Xuping Zhang. WELL-POSEDNESS OF NONLOCAL IMPULSIVE PROBLEMS OF NON-AUTONOMOUS EVOLUTION EQUATIONS WITH DELAY[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 916-936. doi: 10.11948/20250196

Citation:

Huanhuan Wang, Xiaoya Liu, Xuping Zhang. WELL-POSEDNESS OF NONLOCAL IMPULSIVE PROBLEMS OF NON-AUTONOMOUS EVOLUTION EQUATIONS WITH DELAY[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 916-936. doi: 10.11948/20250196

WELL-POSEDNESS OF NONLOCAL IMPULSIVE PROBLEMS OF NON-AUTONOMOUS EVOLUTION EQUATIONS WITH DELAY

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2.
School of Mathematical Sciences, Gansu Minzu Normal University, Gannan 747000, China
3.
Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, China

Author Bio: Email: dahuan0901@126.com(H. Wang); Email: liuxiaoy135@163.com(X. Liu)
Corresponding author: Email: lanyu9986@126.com(X. Zhang)
Fund Project: This work was supported by the Outstanding Youth Science Fund of Gansu Province (No. 24JRRA122), Funds for Innovative Fundamental Research Group Project of Gansu Province (No. 23JRRA684) and Natural Science Foundation of Gansu Province (No. 24JRRA780)

Abstract

Abstract

This paper investigates the existence of extremal mild solutions for nonlocal impulsive problems of non-autonomous evolution equations with delay in ordered Banach spaces. By applying the perturbation technique and monotone iterative method in the presence of lower and upper solutions, we establish the existence of the minimal and maximal mild solutions under suitable monotonicity conditions and noncompactness measure requirements of nonlinear term. Furthermore, we prove the existence of at least one mild solution and obtain the uniqueness of mild solution between the lower and the upper solutions.
- Nonlocal impulsive problems /
- non-autonomous evolution equations /
- mild solution /
- monotone iterative method
MSC: 35R12, 35K45, 47D06, 47H08

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References

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