PERIODIC SOLUTION FOR SECOND-ORDER DAMPED NEUTRAL DIFFERENTIAL EQUATION VIA A FIXED POINT THEOREM OF LERAY-SCHAUDER TYPE

Zhibo Cheng; Lisha Lv; Feifan Li

doi:10.11948/20200041

2021 Volume 11 Issue 4

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Zhibo Cheng, Lisha Lv, Feifan Li. PERIODIC SOLUTION FOR SECOND-ORDER DAMPED NEUTRAL DIFFERENTIAL EQUATION VIA A FIXED POINT THEOREM OF LERAY-SCHAUDER TYPE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1731-1748. doi: 10.11948/20200041

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Zhibo Cheng, Lisha Lv, Feifan Li. PERIODIC SOLUTION FOR SECOND-ORDER DAMPED NEUTRAL DIFFERENTIAL EQUATION VIA A FIXED POINT THEOREM OF LERAY-SCHAUDER TYPE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1731-1748. doi: 10.11948/20200041

PERIODIC SOLUTION FOR SECOND-ORDER DAMPED NEUTRAL DIFFERENTIAL EQUATION VIA A FIXED POINT THEOREM OF LERAY-SCHAUDER TYPE

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Corresponding author: Email address: czb_1982@126.com (Z. Cheng)
Fund Project: Research is supported by National Natural Science Foundation of China (11501170), Technological innovation talents in universities and colleges in Henan Province (21HASTIT025) and Fundamental Research Funds for the Universities of Henan Province (NSFRF170302)

Abstract

Abstract

The aim of this paper is to show that a fixed point theorem of Leray-Schauder type can be applied to damped neutral differential equations. Using the positivity of Green's function, we prove the existence of a positive periodic solution for second-order damped neutral differential equation in the cases that sub-linearity, semi-linearity and super-linearity conditions.
- Periodic solution /
- neutral equation /
- second-order /
- fixed point theorem of Leray-Schauder type
MSC: 34C25, 34K40

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References

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