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

• Datum: 2000
• Hauptverfasser: Mishura, Yu. S., Мішура, Ю. С.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2000
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4459
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We consider a criterion and sufficient conditions for the existence of a solution of the equation $$Z_t x = \frac{{t^{n - 1} x}}{{\left( {n - 1} \right)!}} + \int\limits_0^t {a\left( {t - s} \right)AZ_s xds} $$ in a Banach space X. We determine a resolvent of the Volterra equation by differentia...