# Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

- Volume: 16, Issue: 1, page 75-89
- ISSN: 1509-9407

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topJan Andres, and Tomá Turský. "Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.1 (1996): 75-89. <http://eudml.org/doc/275852>.

@article{JanAndres1996,

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.},

author = {Jan Andres, Tomá Turský},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {Asymptotic estimates; nonhomogeneous equations; inverse operator method; Esclangon's technique; asymptotic estimates; -th order nonhomogeneous ordinary differential equations},

language = {eng},

number = {1},

pages = {75-89},

title = {Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients},

url = {http://eudml.org/doc/275852},

volume = {16},

year = {1996},

}

TY - JOUR

AU - Jan Andres

AU - Tomá Turský

TI - Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1996

VL - 16

IS - 1

SP - 75

EP - 89

AB - 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.

LA - eng

KW - Asymptotic estimates; nonhomogeneous equations; inverse operator method; Esclangon's technique; asymptotic estimates; -th order nonhomogeneous ordinary differential equations

UR - http://eudml.org/doc/275852

ER -

## References

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- [15] R. Reissig, Ein Beschränkheitsatz für gewisse Differentialgleichungen beliebiger Ordnung, Monatsb. Deutsch. Akad. Wiss. Berlin 6 (1964), 407-413. Zbl0121.31501
- [16] K. Rychlík, Introduction to the Analytical Theory of Polynomials with the Real Coefficients, SAV, Praha 1957 (Czech).
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- [20] J. Voráek, Note on paper [1] of S. Sdziwy, Acta UPO 33 (1971), 157-161.

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