Nicolae H. Pavel
Professor, Mathematics





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)
leaving K invariant, then there is a proper subcone  k of K  such that each linear continuous operator  B commuting with A( i.e. AB=BA), leaves K invariant(1972)
It seems that this result is equivalent to Lomonosov's result(in the case K=X)

(To be completed asap.!)

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