Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations
Let $E$ be a finite-dimensional Banach space, let $C^0(R; E)$ be a Banach space of functions continuous and bounded on $R$ and taking values in $E$; let $K:\;C^0(R ,E) → C^0(R, E)$ be a $c$-continuous bounded mapping, let $A:\;E → E$ be a linear continuous mapping, and let $h ∈ C^0(R, E)$. We establ...
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| Datum: | 2010 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2914 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let $E$ be a finite-dimensional Banach space, let $C^0(R; E)$ be a Banach space of functions continuous and bounded on $R$ and taking values in $E$; let $K:\;C^0(R ,E) → C^0(R, E)$ be a $c$-continuous bounded mapping, let $A:\;E → E$ be a linear continuous mapping, and let $h ∈ C^0(R, E)$. We establish conditions for the existence of bounded solutions of the nonlinear equation
$$\frac{dx(t)}{dt} + (Kx)(t)Ax(t) = h(t),\;t ∈ R.$$ |
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