Existence of the boundary in the Chesaro sense of a limited solution of the evolution equation in the Banach space - Gorbachuk , O. L.; Yakonska , N. O. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
An existence criterion for the Cesàro limit (_t → ∞ 1t_0^t y(ξ) dξ ) of a bounded solution y(t) of the problem dy (t)/dt = Ay (t), y(0) = y_0, t[0, ∞), where А 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 (0, δ) belonging to the set of the regular points ρ(А) of the operator A.