Periodic solutions for p-Laplacian neutral differential equation with multiple delay and variable coefficients

被引：0

作者：

Bi, Zhonghua ^{[1
]}

Cheng, Zhibo ^{[1
,2
]}

Yao, Shaowen ^{[1
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Peoples R China

[2] Sichuan Univ, Dept Math, Chengdu, Sichuan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 1期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Neutral operator; p-Laplacian; Periodic solution; Extension of Mawhin's continuation theorem; Singularity; EXISTENCE; SYSTEMS;

D O I：

10.1186/s13662-018-1942-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first discuss some properties of the neutral operator with multiple delays and variable coefficients (Ax)(t) := x(t) - Sigma(n)(i=1)c(i)(t)x(t - delta(i)). Afterwards, by using an extension of Mawhin's continuation theorem, a second order p-Laplacian neutral differential equation (phi(p)(x(t) - Sigma C-n(i=1)i(t)x(t-delta(i))')'= (f) over tilde (t, x(t), x'(t)) Is studied. Some new results on the existence of a periodic solution are obtained. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from those known in the literature.

引用

页数：24

共 19 条

[1]

Anane Aomar, 2012, ELECTRON J DIFFER EQ, V2012, P1

[2] Positive Periodic Solutions for a Kind of Second-Order Neutral Differential Equations with Variable Coefficient and Delay [J].

Cheng, Zhibo ;

Li, Feifan .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (03)

[3] Positive periodic solution of second-order neutral functional differential equations [J].

Cheung, Wing-Sum ;

Ren, Jingli ;

Han, Weiwei .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) :3948-3955

[4] Existence and asymptotic behavior results of periodic solution for discrete-time neutral-type neural networks [J].

Du, Bo ;

Liu, Yurong ;

Abbas, Ibrahim Atiatallah .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2016, 353 (02) :448-461

[5] Periodic solution to p-Laplacian neutral Li,nard type equation with variable parameter [J].

Du, Bo .

MATHEMATICA SLOVACA, 2013, 63 (02) :381-395

[6] Periodic solutions for generalized Lienard neutral equation with variable parameter [J].

Du, Bo ;

Guo, Lixiang ;

Ge, Weigao ;

Lu, Shiping .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (06) :2387-2394

[7]

Gaines R., 1977, LECT NOTE MATH

[8] Periodic solutions for p-Laplacian neutral Lienard equation with a sign-variable coefficient [J].

Gao, Fabao ;

Lu, Shiping ;

Zhang, Wei .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2009, 346 (01) :57-64

[9] An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacain [J].

Ge, WG ;

Ren, JL .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (3-4) :477-488

[10] Some results on second-order neutral functional differential equations with infinite distributed delay [J].

Han, Weiwei ;

Ren, Jingli .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (03) :1393-1406

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