Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations

Abstract

The authors study the existence and uniqueness of a set with $\mathrm{2}kT$-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of $\mathrm{2}kT$-periodic solutions.