2019
Том 71
№ 11

All Issues

Existence of Cesàro limit of bounded solution of evolution equation in banach space

Gorbachuk E. L., Yakons'ka N. O.

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Abstract

An existence criterion for the Cesàro limit $$\left( {\mathop {\lim }\limits_{t \to \infty } \frac{1}{t}\int\limits_0^t {y(\xi )d\xi } } \right)$$ of a bounded solution $y(t)$ of the problem $dy(t)/dt = Ay(t), y(0)=y_0, t ∈ [O, ∞)$, where $ A$ is a closed linear operator with dense domain of definition $D(A)$ in a reflexive Banach space $E$, is obtained under the condition that there exists a sufficiently small interval $(O, δ)$ belonging to the set of the regular points $ρ(A)$ of the operator $A$.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1170-1171.

Citation Example: Gorbachuk E. L., Yakons'ka N. O. Existence of Cesàro limit of bounded solution of evolution equation in banach space // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1279–1280.

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