%0 Journal Article
%T On nonlocal evolution problem for the equation of the first order
%A Byszewski, Ludwik
%A Winiarska, Teresa
%J Czasopismo Techniczne
%V 2013
%R 10.4467/2353737XCT.14.029.2612
%N Nauki Podstawowe Zeszyt 1 NP (4) 2013
%P 19-26
%K evolution Cauchy problem, existence and uniqueness of the solutions, nonlocal conditions
%@ 0011-4561
%D 2013
%U https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/on-nonlocal-evolution-problem-for-the-equation-of-the-first-order
%X 
	The aim of the paper is to prove theorems about the existence and uniqueness of mild
	and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy
	problem. The method of semigroups, the Banach fixed-point theorem and theorems (see [2])
	about the existence and uniqueness of the classical solutions of the first-order differential
	evolution problems in a not necessarily reflexive Banach space are used to prove the existence
	and uniqueness of the solutions of the problems considered. The results obtained are based
	on publications [1–6].