Existence and uniqueness of homoclinic solution for a class of nonlinear second-order differential equations (Q1952899)

Homoclinic solutions are studied for nonlinear second-order differential equations in the form \[ \ddot{u}(t)+g(\dot{u}(t))+h(u(t))=f(t). \] A unique homoclinic orbit is established. The method uses Mawhin's continuation theorem. The authors prove the existence and uniqueness of a family of \(2kT\)-periodic solutions and use this result to obtain the homoclinic orbit as a limit point of this family.