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1996 | 16 | 1 | 75-89
Tytuł artykułu

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

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Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
autor
  • Dept. of Math. Analysis, Fac. of Science, Palacký University, Tomkova 40, 779-00 Olomouc-Hejín, Czech Republic
  • Dept. of Math. Analysis, Fac. of Science, Palacký University, Tomkova 40, 779-00 Olomouc-Hejín, Czech Republic
Bibliografia
  • [1] J. Andres, Langrange stability of higher-order analogy of damped pendulum equations, Acta UPO 106, Phys. 31 (1992), 154-159.
  • [2] J. Andres, On the problem of Hurwitz for shifted polynomials, Acta UPO 106, Phys. 31 (1992), 160-164 (Czech).
  • [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.
  • [4] E.A. Barbashin and V.A. Tabueva, Dynamical Systems with Cylindrical Phase Space, Nauka, Moscow 1969 (Russian).
  • [5] B.F. Bylov, R.E. Vinograd, D.M. Grobman and V. V. Nemytskii, Theory of Liapunov Exponents, Nauka, Moscow 1966 (Russian).
  • [6] L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, Berlin 1959.
  • [7] W.A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath, Boston 1965.
  • [8] E. Esclangon, Sur les intégrales bornées d'une équation différentielle linéaire, C. R. Ac. de Sc., Paris 160 (1915), 775-778.
  • [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.
  • [10] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Nauka, Moscow 1985 (Russian).
  • [11] J. Kaucký, Elementary Methods for Solutions of Ordinary Differential Equations, SAV, Praha 1953 (Czech).
  • [12] W. Kaplan, Ordinary Differential Equations, Addison-Wesley, Reading, Mass., 1940.
  • [13] M.A. Krasnosel'skii, V. Sh. Burd and Yu. S. Kolesov, Nonlinear Almost Periodic Oscillations, Nauka, Moscow 1970 (Russian).
  • [14] B.M. Levitan, Almost-Periodic Functions, GITTL, Moscow 1953 (Russian).
  • [15] R. Reissig, Ein Beschränkheitsatz für gewisse Differentialgleichungen beliebiger Ordnung, Monatsb. Deutsch. Akad. Wiss. Berlin 6 (1964), 407-413.
  • [16] K. Rychlík, Introduction to the Analytical Theory of Polynomials with the Real Coefficients, SAV, Praha 1957 (Czech).
  • [17] G. Sansone, Equazioni differenziali nel campo reale II, N. Zanichelli, Bologna 1949.
  • [18] S. Sdziwy, Asymptotic properties of solutions of nonlinear differential equations of higher order, Zeszyty Nauk. Univ. Jagiel. 131 (1966), 69-80.
  • [19] P.N.V. Tu, Dynamical Systems (An Introduction with Applications in Economics and Biology), Springer, Berlin 1992.
  • [20] J. Voráek, Note on paper [1] of S. Sdziwy, Acta UPO 33 (1971), 157-161.
Typ dokumentu
Bibliografia
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