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.
"HOMOCLINIC SOLUTIONS FOR A CLASS OF NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS WITH TIME-VARYING DELAYS." Taiwanese J. Math. 17 (6) 2149 - 2161, 2013. https://doi.org/10.11650/tjm.17.2013.3198