HOMOCLINIC SOLUTIONS FOR A CLASS OF NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS WITH TIME-VARYING DELAYS

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of homoclinic solutions for a class of nonlinear second-order differential equations with time-varying delays. Moreover, we give an example to illustrate th...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 6; pp. 2149 - 2161
Main Authors Li, Yongkun, Yang, Li
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2013
Subjects
Coincidence
Differential equations
Existence theorems
Second order differential equations
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Summary:In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of homoclinic solutions for a class of nonlinear second-order differential equations with time-varying delays. Moreover, we give an example to illustrate the feasibility of obtained results. Our results are completely new. 2010Mathematics Subject Classification: 34K13, 34C37. Key words and phrases: Homoclinic solutions, Coincidence degree, Differential equations Time-varying delays.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.3198