Among the results I have obtained, I mention:
1. Every ultimately bounded T-periodic system in R^n : x'(t)= f(t,x(t)) is uniformly bounded, uniform ultimately bounded and admits a T-periodic solution (i.e. the system has harmonic oscillations). One assumes that the function f = f(t,x) is continuos on R^2 and guarantees the existence and uniqueness of the solution to the Cauchy problem for system.
2. I have introduced the notion of weak ultimately bounded systems.
3. Let X be an infinite-dimensional Banach space and let K be a closed
cone with non-empty interior. If A is a completely continuous
operator from X into itself ( A non identically zero)
(To be completed asap.!)