On some possible extensions of Massera's theorem

G. Makay, Bolyai Institute, University of Szeged, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 16. (2000), pp. 1-8.

Abstract: In this paper we consider ordinary and functional differential equations with $T$-periodic right hand side and look at some conjectures on proving the existence of a periodic solution. One of the ''best'' conditions to obtain a periodic solution is the existence of a bounded solution, because it would be then not only a sufficient but also a neccessary condition. We take one step in the direction to prove this conjecture.

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