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THE EXISTENCE OF A WEAK SOLUTION OF THE SEMILINEAR FIRST-ORDER DIFFERENTIAL EQUATION IN A BANACH SPACE

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PL
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PL
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.
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online
2015-04-09
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bwmeta1.element.ojs-nameId-6e3e8ea9-5a94-37a7-828b-e6cd5da23db6-year-2015-article-1612
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