EXISTENCE OF TIME PERIODIC SOLUTIONS TO PARABOLIC DELAYED EVOLUTION EQUATION IN ORDERED BANACH SPACE

Shengbin Yang; Yongxiang Li

doi:10.11948/20250279

2026 Volume 16 Issue 5

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Shengbin Yang, Yongxiang Li. EXISTENCE OF TIME PERIODIC SOLUTIONS TO PARABOLIC DELAYED EVOLUTION EQUATION IN ORDERED BANACH SPACE[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2333-2350. doi: 10.11948/20250279

Citation:

Shengbin Yang, Yongxiang Li. EXISTENCE OF TIME PERIODIC SOLUTIONS TO PARABOLIC DELAYED EVOLUTION EQUATION IN ORDERED BANACH SPACE[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2333-2350. doi: 10.11948/20250279

EXISTENCE OF TIME PERIODIC SOLUTIONS TO PARABOLIC DELAYED EVOLUTION EQUATION IN ORDERED BANACH SPACE

Shengbin Yang^1, ,,
Yongxiang Li^1,

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Author Bio: Email: liyxnwnu@163.com(Y. Li)
Corresponding author: Email: yangshengbin2022@163.com(S. Yang)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061062, 12161080)

Abstract

Abstract

The purpose of the article is to systematically research time $\omega$-periodic problem to the general parabolic delayed evolution equation. First of all, by applying theory of operator semigroup, the Schauder fixed point theorem, and monotone iterative method, the existence and uniqueness results of $\omega$-periodic mild solutions and positive mild solutions to the abstract evolution equation with delay are gained when nonlinear term satisfies some suitable ordered conditions. Next, we use the abstract results to get similar results of periodic problem to the parabolic evolution equation with finite delay, which improves and generalizes the related work of this fields. Ultimately, two examples to parabolic delayed evolution equation are presented.
- Parabolic delayed evolution equation /
- periodic solution /
- existence and uniqueness /
- Schauder fixed point /
- ordered Banach space
MSC: 34K30, 34K40, 47D03, 35A09

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References

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