Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales by Murat Adıvar & Youssef N. Raffoul

Author:Murat Adıvar & Youssef N. Raffoul
Language: eng
Format: epub
ISBN: 9783030421175
Publisher: Springer International Publishing

We show that y(r) is bounded away from zero. Suppose that it is not true, then there is a sequence {r n} tending to infinity monotonically such that y(r n) → 0, a contradiction to y T(r)Dy(r) ≤ y0TDy 0 < 0. Thus there is β > 0 with so that implying that as r →∞. This contradicts and completes the proof.

We now prove instability result for the zero solution of (5.1.22). For this suppose D be a positive definite symmetric matrix satisfying

(5.1.24)

Theorem 5.1.6

Suppose that (5.1.24) holds for some symmetric matrix D and that there is a constant M > 0 such that

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