Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 2506463
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Abstract | References | Similar articles | Additional information

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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