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

Jan Andres; Tomá Turský

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

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

Abstract

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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.

How to cite

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Jan 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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  1. [1] J. Andres, Langrange stability of higher-order analogy of damped pendulum equations, Acta UPO 106, Phys. 31 (1992), 154-159. 
  2. [2] J. Andres, On the problem of Hurwitz for shifted polynomials, Acta UPO 106, Phys. 31 (1992), 160-164 (Czech). 
  3. [3] J. Andres and V. Vlek, Asymptotic behaviour of solutions to the n-th order nonlinear differential equation under forcing, Rend. Ist. Mat. Univ. Trieste 21 (1) (1989), 128-143. Zbl0753.34020
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  7. [7] W.A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath, Boston 1965. 
  8. [8] E. Esclangon, Sur les intégrales bornées d'une équation différentielle linéaire, C. R. Ac. de Sc., Paris 160 (1915), 775-778. Zbl45.0475.02
  9. [9] J.O.C. Ezeilo, A boundedness theorem for a certain n-th order differential equation, Ann. Mat. Pura Appl. 4 (88) (1971), 135-142. Zbl0223.34027
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  12. [12] W. Kaplan, Ordinary Differential Equations, Addison-Wesley, Reading, Mass., 1940. 
  13. [13] M.A. Krasnosel'skii, V. Sh. Burd and Yu. S. Kolesov, Nonlinear Almost Periodic Oscillations, Nauka, Moscow 1970 (Russian). 
  14. [14] B.M. Levitan, Almost-Periodic Functions, GITTL, Moscow 1953 (Russian). 
  15. [15] R. Reissig, Ein Beschränkheitsatz für gewisse Differentialgleichungen beliebiger Ordnung, Monatsb. Deutsch. Akad. Wiss. Berlin 6 (1964), 407-413. Zbl0121.31501
  16. [16] K. Rychlík, Introduction to the Analytical Theory of Polynomials with the Real Coefficients, SAV, Praha 1957 (Czech). 
  17. [17] G. Sansone, Equazioni differenziali nel campo reale II, N. Zanichelli, Bologna 1949. 
  18. [18] S. Sdziwy, Asymptotic properties of solutions of nonlinear differential equations of higher order, Zeszyty Nauk. Univ. Jagiel. 131 (1966), 69-80. 
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  20. [20] J. Voráek, Note on paper [1] of S. Sdziwy, Acta UPO 33 (1971), 157-161. 

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