EXISTENCE AND UNIQUENESS OF DISCONTINUOUS PERIODIC ORBITS IN SECOND ORDER DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT IMPULSES

Fangfang Jiang

doi:10.11948/20210029

2022 Volume 12 Issue 1

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Fangfang Jiang. EXISTENCE AND UNIQUENESS OF DISCONTINUOUS PERIODIC ORBITS IN SECOND ORDER DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT IMPULSES[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 69-86. doi: 10.11948/20210029

Citation:

Fangfang Jiang. EXISTENCE AND UNIQUENESS OF DISCONTINUOUS PERIODIC ORBITS IN SECOND ORDER DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT IMPULSES[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 69-86. doi: 10.11948/20210029

EXISTENCE AND UNIQUENESS OF DISCONTINUOUS PERIODIC ORBITS IN SECOND ORDER DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT IMPULSES

Fangfang Jiang^1, ,

1.
School of Science, Jiangnan University, Wuxi, 214122, China

Corresponding author: Fangfang Jiang, E-mail: jiangfangfang87@126.com
Fund Project: The author was supported by National Natural Science Foundation of China (11701224) and Natural Science Foundation of JiangSu Province-Provincial Youth Foundation (BK20170168)

Abstract

Abstract

In this paper, we are concerned with the existence and uniqueness of discontinuous periodic orbits for a class of second order impulsive differential equations with state-dependent jumps. we apply geometric method to estimate the time mapping of the equation, and then by using Poincaré-Bohl fixed point theorem to obtain some existence criteria under assumptions that the nonlinear term satisfies linear growth conditions. And, the uniqueness of the discontinuous periodic orbit is further proved. Finally, several specific impulsive functions are presented in examples to illustrate the obtained results.
- State-dependent impulse /
- Poincaré-Bohl fixed point theorem /
- discontinuous periodic orbit /
- existence /
- uniqueness
MSC: 34A12, 34A34, 34C25

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References

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