Existence of solutions of abstract volterra equations in a banach space and its subsets
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...
Збережено в:
| Дата: | 2000 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2000
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4459 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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 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). |
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