Homoclinic solutions for a class of nonlinear second-order differential equations with time-varying delays
type: Item
instance of: scholarly article
title: Homoclinic solutions for a class of nonlinear second-order differential equations with time-varying delays
zbMATH Open document ID: 1288.34058
author: Li Yang
author: Yongkun Li
published in: Taiwanese Journal of Mathematics
publication date: 2014-01-29T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/3198
reviewed by: Xueyan Liu
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6252023
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: coincidence degree
zbMATH Keywords: differential equations
zbMATH Keywords: time-varying delays
MaRDI profile type: Publication
OpenAlex ID: W2153306824
DOI: 10.11650/TJM.17.2013.3198
review text: The paper studies the following second-order differential equation with time-varying delays NEWLINE\[NEWLINE\begin{aligned} & x''(t)+a(t)g(x'(t))\\ & +\sum_{i=1}^n b_i(t)h_i (x(t-\tau_1(t)),x(t-\tau_2(t)),\ldots,x(t-\tau_n(t)))=f(t), \end{aligned}NEWLINE\]NEWLINE where the functions \(a,b_i,\tau_i,f,g,h_i\), are continuous on \(\mathbb R\), \(a,b_i\) are \(2T\)-periodic, positive, and bounded, \(\tau_i\)'s are positive for \(i=1,\ldots, n\).NEWLINENEWLINEThe paper mainly applies Mawhin's continuation theorem of coincidence degree theory to obtain some sufficient criteria for the existence of homoclinic solutions of the above equation and then provides an example.
description: scientific article; zbMATH DE number 6252023