Existence of forced oscillations for some nonlinear differential equations

Abstract

This article studies the existence of T-periodic solutions for systems of nonlinear second order ordinary differential equations. Assuming function V to be superquadratic, it is shown that this system possesses infinitely many T-periodic solutions. The proof of this result rests on showing that certain homotopy groups of level sets of the functional associated with the system are not trivial. Some more general results concerning systems of another type are also presented.