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Estimates for the Green functions of nonautonomous higher order differential equations

Author(s): Michael Gil'
Journal: Proc. Amer. Math. Soc. 137 (2009), 3045-3055.
MSC (2000): Primary 34A30, 34D20
Posted: February 23, 2009
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Abstract: We consider the equation

$\displaystyle \sum_{k=0}^{n} a_k(t)x^{(n-k)}(t)=0\;\;(t > 0),$

where $ a_0(t)\equiv 1;\;a_k(t)\;(k=1, ..., n)$ are bounded continuous functions. It is assumed that all the roots $ r_k(t)\;\;(k=1, ..., n)$ of the polynomial $ z^n+a_1(t)z^{n-1}+ ... +a_n(t)$ are real for all $ t\geq 0$. Sharp estimates for the Green function to the Cauchy problem and their derivatives are derived.

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Additional Information:

Michael Gil'
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Email: gilmi@cs.bgu.ac.il

DOI: 10.1090/S0002-9939-09-09829-3
PII: S 0002-9939(09)09829-3
Keywords: Ordinary differential equations, linear nonautonomous equations, estimates for Green functions
Received by editor(s): August 12, 2008,
Received by editor(s) in revised form: November 17, 2008
Posted: February 23, 2009
Additional Notes: This research was supported by the Kamea Fund of Israel
Communicated by: Bryna Kra
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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