<![CDATA[WUJ]]><![CDATA[info@ejournals.eu]]>http://www.ejournals.eu/20200530ejournals.eu.article.458003010610.4467/2353737XCT.14.300.338820<![CDATA[operator, semigroup, weak solution]]>00ED031001Number10102<![CDATA[Czasopismo Techniczne]]>03<![CDATA[2014]]>01<![CDATA[Nauki Podstawowe Zeszyt 2 NP (16) 2014]]>1A01<![CDATA[Mariusz Jużyniec]]>0101<![CDATA[THE EXISTENCE OF A WEAK SOLUTION OF THE SEMILINEAR
FIRST-ORDER DIFFERENTIAL EQUATION IN A BANACH
SPACE]]>01en00303020PLN03<![CDATA[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.]]>012015020915000401http://dx.doi.org/10.4467/2353737XCT.14.300.3388