Solvability of semilinear differential equations with singularity
Local theorems on the existence of solutions of the Cauchy problem for the singular equations of the form $$ \frac{d}{dt}(Au(t)) + Bu(t) = f(t, u)$$ in Banach spaces are proved. The conditions for the solvability depend on a type of the singularity of the sheaf $\lambda A + B$ of closed linear opera...
Збережено в:
| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2008
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3152 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Local theorems on the existence of solutions of the Cauchy problem for the singular equations of the form
$$ \frac{d}{dt}(Au(t)) + Bu(t) = f(t, u)$$
in Banach spaces are proved. The conditions for the solvability depend on a type of the singularity of the sheaf $\lambda A + B$ of closed linear operators $A, B$. Examples and applications
to finite-dimensional differential algebraic equations, infinite systems of differential equations, and partial differential equations of non-Kovalevskaya type are presented. |
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