Existence of solutions of abstract volterra equations in a banach space and its subsets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Existence of solutions of abstract volterra equations in a banach space and its subsets

Authors:

Yu. S. Mishura

Affiliation:

(1) Institute of Mathematics, Ukranian Academy of Sciences, Kiev

Abstract:

We consider a criterion and sufficient conditions for the existence of a solution of the equation

$Z_t x = frac{{t^{n - 1} x}}{{left( {n - 1} right)!}} + intlimits_0^t {aleft( {t - s} right)AZ_s xds}$

in a Banach space X. We determine a resolvent of the Volterra equation by differentiating the considered solution on subsets of X. We consider the notion of "incomplete" resolvent and its properties. We also weaken the Priiss conditions on the smoothness of the kernel a in the case where A generates a C ₀-semigroup and the resolvent is considered on D(A).

Keywords:

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