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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 timevarying 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