@article{9516dc46-3a05-431d-bd4f-656292618c78,
author = {Mariusz Jużyniec},
title = {THE EXISTENCE OF A WEAK SOLUTION OF THE SEMILINEAR
	FIRST-ORDER DIFFERENTIAL EQUATION IN A BANACH
	SPACE},
journal = {Czasopismo Techniczne},
volume = {2014},
number = {Nauki Podstawowe Zeszyt 2 NP (16) 2014},
year = {2015},
issn = {0011-4561},
pages = {59-62},keywords = {operator; semigroup; weak solution},
abstract = {This paper is devoted to the investigation of the existence and uniqueness of a suitably defined weak solution of the abstract semilinear value problem u_ (t) = Au(t) + f(t; u(t)); u(0) = x with x 2 X; where X is a Banach space. We are concerned with two types of solutions: weak and mild. Under the assumption that A is the generator of a strongly continuous semigroup of linear, bounded operators, we also establish sufficient conditions such that if u is a weak (mild) solution of the initial value problem, then u is a mild (weak) solution of that problem.},
doi = {10.4467/2353737XCT.14.300.3388},
url = {https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/the-existence-of-a-weak-solution-of-the-semilinear-first-order-differential-equation-in-a-banach-space}
}