Oscillation theorems for neutral differential equations with the quasi-derivatives

Miroslava Růžičková; E. Špániková

Archivum Mathematicum (1994)

  • Volume: 030, Issue: 4, page 293-300
  • ISSN: 0044-8753

Abstract

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The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives L n [ x ( t ) + ( - 1 ) r P ( t ) x ( g ( t ) ) ] + δ Q ( t ) f ( x ( h ( t ) ) ) = 0 , where n ≥ 2 , r ∈ { 1 , 2 } , and δ = ± 1 . There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.

How to cite

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Růžičková, Miroslava, and Špániková, E.. "Oscillation theorems for neutral differential equations with the quasi-derivatives." Archivum Mathematicum 030.4 (1994): 293-300. <http://eudml.org/doc/247543>.

@article{Růžičková1994,
abstract = {The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.},
author = {Růžičková, Miroslava, Špániková, E.},
journal = {Archivum Mathematicum},
keywords = {neutral differential equation; oscillatory (nonoscillatory) solution; quasi derivatives; nonlinear neutral differential equations with quasiderivatives},
language = {eng},
number = {4},
pages = {293-300},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillation theorems for neutral differential equations with the quasi-derivatives},
url = {http://eudml.org/doc/247543},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Růžičková, Miroslava
AU - Špániková, E.
TI - Oscillation theorems for neutral differential equations with the quasi-derivatives
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 4
SP - 293
EP - 300
AB - The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x(t)+(-1)^r P(t) x(g(t))]+\delta Q(t) f(x(h(t))) = 0,$ where $\ n \ge 2,\ r \in \lbrace 1,2\rbrace ,\ $ and $ \delta = \pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.
LA - eng
KW - neutral differential equation; oscillatory (nonoscillatory) solution; quasi derivatives; nonlinear neutral differential equations with quasiderivatives
UR - http://eudml.org/doc/247543
ER -

References

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  1. On the oscillation of an n th-order nonlinear neutral delay differential equation, J. Comp. Appl. Math. 41 (1992), 35-40. (1992) MR1181706
  2. Oscillation properties of first order nonlinear functional differential equations of neutral type, Diff. and Int. Equat. (1991), 425-436. (1991) MR1081192
  3. Oscillatory properties of functional differential systems of neutral type, Czech. Math. J. 43 (1993), 649-662. (1993) MR1258427
  4. Nonoscillatory solutions of differential equations with deviating argument, Czech. Math. J. 36 (111) (1986), 93-107. (1986) MR0822871
  5. Oscillation of bounded solutions of neutral differential equations, Appl. Math. Lett. 2 (1993), 43-46. (1993) MR1347773

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