STUDY ON A KIND OF $P$-LAPLACIAN NEUTRAL DIFFERENTIAL EQUATION WITH MULTIPLE VARIABLE COEFFICIENTS

Zhibo Cheng; Zhonghua Bi

doi:10.11948/2156-907X.20170234

2019 Volume 9 Issue 2

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Zhibo Cheng, Zhonghua Bi. STUDY ON A KIND OF $P$-LAPLACIAN NEUTRAL DIFFERENTIAL EQUATION WITH MULTIPLE VARIABLE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 501-525. doi: 10.11948/2156-907X.20170234

Citation:

Zhibo Cheng, Zhonghua Bi. STUDY ON A KIND OF $P$-LAPLACIAN NEUTRAL DIFFERENTIAL EQUATION WITH MULTIPLE VARIABLE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 501-525. doi: 10.11948/2156-907X.20170234

STUDY ON A KIND OF $P$-LAPLACIAN NEUTRAL DIFFERENTIAL EQUATION WITH MULTIPLE VARIABLE COEFFICIENTS

Zhibo Cheng^1,2, ,,
Zhonghua Bi¹

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
2.
Department of Mathematics, Sichuan University, Chengdu, 610064, China

Corresponding author: Email address: czb_1982@126.com (Z. Cheng)
Fund Project: Foundation of China (11501170), China Postdoctoral Science Foundation funded project (2016M590886) and the Universities of Henan Provience (NSFRF170302)

Abstract

Abstract

In this paper, we first discuss some properties of the neutral operator with multiple variable coefficients $(Ax)(t): = x(t)-\sum\limits_{i = 1}^{n}c_i(t)x(t-\delta_i)$. Afterwards, by using an extension of Mawhin's continuation theorem, a kind of second order $p$-Laplacian neutral differential equation with multiple variable coefficients as follows $\left(\phi_p\left(x(t)-\sum\limits_{i = 1}^{n}c_i(t)x(t-\delta_i)\right)'\right)' = \tilde{f}(t,x(t),x'(t)) $ is studied. Finally, we consider the existence of periodic solutions for two kinds of second-order $p$-Laplacian neutral Rayleigh equations with singularity and without singularity. Some new results on the existence of periodic solutions are obtained. It is worth noting that $c_i$ ($i = 1, \cdots, n$) are no longer constants which are different from the corresponding ones of past work.
- Neutral operator with multiple variable coefficients /
- $p$-Laplacian /
- periodic solution /
- extension of Mawhin's continuation theorem /
- singularity
MSC: 34C25, 34B16, 34B18

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References

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