Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A minimal decay rate for solutions of stable $n$th order homogeneous differential equations with constant coefficients

Author: David W. Kammler
Journal: Proc. Amer. Math. Soc. 48 (1975), 145-151
MSC: Primary 34C10
MathSciNet review: 0369810
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we establish the existence of an envelope function (depending only on $n$ and $\alpha > 0$) which provides a pointwise bound on the size of any normalized solution $y$ of any homogeneous $n$th order differential equation with constant coefficients for which the roots of the corresponding characteristic polynomial have real parts which do not exceed $- \alpha$. An explicit representation for this envelope is obtained in the special case where these roots are further constrained to be real valued.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10

Additional Information

Keywords: Minimal decay rate for exponential sums, Chebyshev polynomial on <!– MATH $[0, + \infty )$ –> <IMG WIDTH="73" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$[0, + \infty )$"> with exponential weight
Article copyright: © Copyright 1975 American Mathematical Society