Том 71
№ 11

All Issues

Yakons'ka N. O.

Articles: 1
Brief Communications (Ukrainian)

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

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

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1279–1280

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 $A$.