Branching of t-periodic solutions for a certain class of ordinary differential equations^*

_*This research was sponsored in part by the National Science Foundation under Contract INT-8602537 and by FONDECYT, Research grant 546-88 and by the DTI, U. of Chile. The first author also received support from B.S.U. Faculty Research Grant 681A036

Abstract

Sufficient conditions are given for the existence of periodic solutions of the weakly forced ODE X¹ = f(x) + F(t, x, λ) where x λ R², λ is a small parameter in a Banach space and F is T-periodic in its first variable. Some illustrative examples are provided

Keywords:

• Periodic Solutions

AMS(MOS)::

• 34C25

_*This research was sponsored in part by the National Science Foundation under Contract INT-8602537 and by FONDECYT, Research grant 546-88 and by the DTI, U. of Chile. The first author also received support from B.S.U. Faculty Research Grant 681A036

_*This research was sponsored in part by the National Science Foundation under Contract INT-8602537 and by FONDECYT, Research grant 546-88 and by the DTI, U. of Chile. The first author also received support from B.S.U. Faculty Research Grant 681A036

Notes

_*This research was sponsored in part by the National Science Foundation under Contract INT-8602537 and by FONDECYT, Research grant 546-88 and by the DTI, U. of Chile. The first author also received support from B.S.U. Faculty Research Grant 681A036