Perturbing Uniform Ultimate Bounded Differential Systems
SIAM Journal on Mathematical Analysis1972Vol. 3(2), pp. 358–370
Abstract
We obtain results on the eventual uniform boundedness and eventual uniform ultimate boundedness of solutions of the differential equation \[ \dot x = f(t,x) + g(t,x)\] given that solutions of the equation $\dot x = f(t,x)$ are uniformly bounded and uniformly ultimately bounded. By assuming various regularity conditions on f we obtain admissible classes of g such that the boundedness properties are preserved. By use of various examples the admissible classes of g are shown to be “maximal.”
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