THE METHOD OF LOWER AND UPPER SOLUTIONS FOR DAMPED ELASTIC SYSTEMS IN BANACH SPACES

Haide Gou; Yongxiang Li

doi:10.11948/20180267

2020 Volume 10 Issue 2

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Haide Gou, Yongxiang Li. THE METHOD OF LOWER AND UPPER SOLUTIONS FOR DAMPED ELASTIC SYSTEMS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 495-513. doi: 10.11948/20180267

Citation:

Haide Gou, Yongxiang Li. THE METHOD OF LOWER AND UPPER SOLUTIONS FOR DAMPED ELASTIC SYSTEMS IN BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 495-513. doi: 10.11948/20180267

THE METHOD OF LOWER AND UPPER SOLUTIONS FOR DAMPED ELASTIC SYSTEMS IN BANACH SPACES

Haide Gou^1, ,,
Yongxiang Li^1, ,

1.
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

Corresponding authors: Email address:842204214@qq.com(H. Gou); Email address:liyxnwnu@163.com(Y. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (11661071)

Abstract

Abstract

In this paper, we are concerned with the initial value problem of a class of damped elastic systems in an order Banach spaces E. By employing the method of lower and upper solutions, we discuss the existence of extremal mild solutions between lower and upper mild solutions for such problem with the associated semigroup is equicontinuous. In addition, two examples are given to illustrate our results.
- Damped elastic systems /
- extremal mild solution /
- the method of lower and upper solution /
- measure of noncompactness
MSC: 34G20, 34K30, 35B10, 47D06

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