%0 Journal Article
%T Existence of the solution to a nonlocal-in-time evolutional problem
%A Dmytro Sytnyk
%A Volodymyr Makarov
%A Vitalii Vasylyk
%J Mathematics
%D 2014
%I arXiv
%X This work is devoted to the study of a nonlocal-in-time evolutional problem for the first order differential equation in Banach space. Our primary approach, although stems from the convenient technique based on the reduction of a nonlocal problem to its classical initial value analogue, uses more advanced analysis. That is a validation of the correctness in definition of the general solution representation via the Dunford-Cauchy formula. Such approach allows us to reduce the given existence problem to the problem of locating zeros of a certain entire function. It results in the necessary and sufficient conditions for the existence of a generalized (mild) solution to the given nonlocal problem. Aside of that we also present new sufficient conditions which in the majority of cases generalize existing results.
%U http://arxiv.org/abs/1406.5417v1