Discussiones Mathematicae Differential Inclusions 16(1) (1996) 75-89

[BIBTex]

ASYMPTOTIC ESTIMATES OF SOLUTIONS AND THEIR DERIVATIVES FOR n-th ORDER NONHOMOGENEOUS ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

Jan Andres and Tomá Turský

Dept. of Math. Analysis, Fac. of Science, Palacký University
Tomkova 40, 779-00 Olomouc-Hejín, Czech Republic

Abstract

Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ODEs with constant coefficients are obtained, provided the associated characteristic polynomial is (asymptotically) stable. Assuming, additionally, the stability of the so called ``shifted polynomials'' (see below) to the characteristic one, the estimates can be still improved.

Keywords: Asymptotic estimates, nonhomogeneous equations, inverse operator method, Esclangon's technique.

1991 Mathematics Subject Classification: 34A30, 34D05, 34D40.

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