Oscillatory properties of some classes of nonlinear differential equations

Milan Medveď

Mathematica Bohemica (1992)

  • Volume: 117, Issue: 2, page 123-131
  • ISSN: 0862-7959

Abstract

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A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by n -th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.

How to cite

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Medveď, Milan. "Oscillatory properties of some classes of nonlinear differential equations." Mathematica Bohemica 117.2 (1992): 123-131. <http://eudml.org/doc/29064>.

@article{Medveď1992,
abstract = {A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by $n$-th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.},
author = {Medveď, Milan},
journal = {Mathematica Bohemica},
keywords = {system of differential equations; nonoscillatory; oscillatory properties; oscillation; nonlinear differential equation; system of differential equations; nonoscillatory; oscillatory properties},
language = {eng},
number = {2},
pages = {123-131},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillatory properties of some classes of nonlinear differential equations},
url = {http://eudml.org/doc/29064},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Medveď, Milan
TI - Oscillatory properties of some classes of nonlinear differential equations
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 2
SP - 123
EP - 131
AB - A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by $n$-th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.
LA - eng
KW - system of differential equations; nonoscillatory; oscillatory properties; oscillation; nonlinear differential equation; system of differential equations; nonoscillatory; oscillatory properties
UR - http://eudml.org/doc/29064
ER -

References

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  1. S. Busenberg D. Fisher M. Martelli, 10.1080/00029890.1989.11972137, The Amer. Math. Monthly 96 no. 1 (1989), 5-17. (1989) MR0979590DOI10.1080/00029890.1989.11972137
  2. J. Guckenheimer P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983. (1983) MR0709768
  3. M. Medveď, Sufficient condition for the non-oscillation of the non-homogeneous linear n-th order differential equation, Matematický časopis 18 no. 2 (1968), 99-104. (1968) MR0245902
  4. M. Medveď, Note to the properties of solutions of the nonhomogeneous linear differential equation of the 2 nd order, Acta Facultatis Rerum Naturalium Universitatis Comenianae Mathematica 19 (1968), 191-195. (In Slovak.) (1968) MR0262636
  5. F. G. Tricomi, Differential Equations, Blackie and Son Limited, 1961. (1961) Zbl0101.05904MR0138812
  6. V. Šeda, On a class of nonlinear n-th order differential equations, Czechosl. Math. J. 39 (114) (19S9), 350-368. (19S9) MR0992139
  7. M. Švec, On various properties of the solutions of third and fourth order linear differential equations, Differential Equations and Their Applications (Proc. Conf., Prague 1962), Publ. House of the Czechosl. Acad. Sci., Prague, Academic Press, New York, 1963, pp. 187-198. (1962) MR0174825

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