The periods of the Volterra-Lotka system.
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.
The objective of this note is the announcement of two results of Ambrosetti-Prodi type concerning the existence of periodic (respectively bounded) solutions of the first order differential equation x' = f (t,x).
Applying a nonsmooth version of a three critical points theorem of Ricceri, we prove the existence of three periodic solutions for an ordinary differential inclusion depending on two parameters.
This paper extends some known results on the boundedness of solutions and the existence of periodic solutions of certain vector equations to matrix equations.