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1999 Singular differential equations with delay
Angelo Favini, Luciano Pandolfi, Hiroki Tanabe
Differential Integral Equations 12(3): 351-371 (1999).

Abstract

The differential equation $d(Mu(t))/dt=-Lu(t)+L_1u(t-1), $ $t\geq0, $ $u(t)=\varphi(t),$ $ -1\leq t\leq0$, for a given strongly continuous $X$-valued function $\varphi$ on $[-1,0]$ is studied, where $M, L, L_1$ are closed linear operators from the complex Banach space $X$ into itself, and $L$ is invertible. Though already in the finite dimensional case in general existence of continuous solutions on $[-1,\infty)$ may fail or it is possible to have continuous solutions only on a finite interval, we indicate classes of operators for which existence results analogous to the ones for regular equations $M=I$ hold. In particular, solutions are given explicitly by a recovery formula.

Citation

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Angelo Favini. Luciano Pandolfi. Hiroki Tanabe. "Singular differential equations with delay." Differential Integral Equations 12 (3) 351 - 371, 1999.

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1022.35080
MathSciNet: MR1674398

Subjects:
Primary: 34K30
Secondary: 35R10, 47N20

Rights: Copyright © 1999 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.12 • No. 3 • 1999
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