Global monotonicity and oscillation for second order differential equation

Miroslav Bartušek; Mariella Cecchi; Zuzana Došlá; Mauro Marini

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 209-222
  • ISSN: 0011-4642

Abstract

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Oscillatory properties of the second order nonlinear equation ( r ( t ) x ' ) ' + q ( t ) f ( x ) = 0 are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.

How to cite

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Bartušek, Miroslav, et al. "Global monotonicity and oscillation for second order differential equation." Czechoslovak Mathematical Journal 55.1 (2005): 209-222. <http://eudml.org/doc/30939>.

@article{Bartušek2005,
abstract = {Oscillatory properties of the second order nonlinear equation \[ (r(t)x^\{\prime \})^\{\prime \}+q(t)f(x)=0 \] are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.},
author = {Bartušek, Miroslav, Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro},
journal = {Czechoslovak Mathematical Journal},
keywords = {second order nonlinear differential equation; oscillatory solution; nonoscillatory solution; coexistence problem; second-order nonlinear differential equation; oscillatory solution; nonoscillatory solution; coexistence problem},
language = {eng},
number = {1},
pages = {209-222},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global monotonicity and oscillation for second order differential equation},
url = {http://eudml.org/doc/30939},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Bartušek, Miroslav
AU - Cecchi, Mariella
AU - Došlá, Zuzana
AU - Marini, Mauro
TI - Global monotonicity and oscillation for second order differential equation
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 209
EP - 222
AB - Oscillatory properties of the second order nonlinear equation \[ (r(t)x^{\prime })^{\prime }+q(t)f(x)=0 \] are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.
LA - eng
KW - second order nonlinear differential equation; oscillatory solution; nonoscillatory solution; coexistence problem; second-order nonlinear differential equation; oscillatory solution; nonoscillatory solution; coexistence problem
UR - http://eudml.org/doc/30939
ER -

References

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  14. On asymptotic decaying solutions for a class of second order differential equations, Arch. Math. (Brno) 35 (1999), 275–284. (1999) Zbl1048.34088MR1725843
  15. Asymptotic properties of solutions of the systems of nonlinear nonautonomous ordinary differential equations, (1993), Adygeja Publ., Maikop. (Russian) (1993) 
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