Periodic solutions of polynomial non-autonomous differential equations.
Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.
The existence of a non-trivial periodic solution for the autonomous Rayleigh equation is proved, assuming conditions which do not imply that has a definite sign for large. A similar result is obtained for the periodically forced equation .
A criterion for the existance of periodic solutions of an ordinary differential equation of order k proved by J. Andres and J. Vorâcek for k = 3 is extended to an arbitrary odd k.
Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .