Oscillation of nonlinear differential systems with retarded arguments

Beatrix Bačová; Božena Dorociaková

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 255-262
  • ISSN: 0011-4642

Abstract

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In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form y i ' ( t ) - p i ( t ) y i + 1 ( t ) = 0 , i = 1 , 2 , , n - 2 , y n - 1 ' ( t ) - p n - 1 ( t ) | y n ( h n ( t ) ) | α s g n [ y n ( h n ( t ) ) ] = 0 , y n ' ( t ) s g n [ y 1 ( h 1 ( t ) ) ] + p n ( t ) | y 1 ( h 1 ( t ) ) | β 0 , where n 3 is odd, α > 0 , β > 0 .

How to cite

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Bačová, Beatrix, and Dorociaková, Božena. "Oscillation of nonlinear differential systems with retarded arguments." Czechoslovak Mathematical Journal 55.1 (2005): 255-262. <http://eudml.org/doc/30942>.

@article{Bačová2005,
abstract = {In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form \[ y^\{\prime \}\_i(t)-p\_i(t)y\_\{i+1\}(t)=0, \quad i=1,2,\dots , n-2, y^\{\prime \}\_\{n-1\}(t)-p\_\{n-1\}(t)|y\_n(h\_n(t))|^\alpha \mathop \{\mathrm \{s\}gn\}[y\_n(h\_n(t))]=0, y^\{\prime \}\_n(t) \mathop \{\mathrm \{s\}gn\}[y\_1(h\_1(t))]+p\_n(t)|y\_1(h\_1(t))|^\beta \, \le 0, \] where $ n\ge 3 $ is odd, $ \alpha >0$, $ \beta >0$.},
author = {Bačová, Beatrix, Dorociaková, Božena},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear differential system; oscillatory (nonoscillatory) solution; nonlinear differential system; oscillatory (nonoscillatory) solution},
language = {eng},
number = {1},
pages = {255-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of nonlinear differential systems with retarded arguments},
url = {http://eudml.org/doc/30942},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Bačová, Beatrix
AU - Dorociaková, Božena
TI - Oscillation of nonlinear differential systems with retarded arguments
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 255
EP - 262
AB - In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form \[ y^{\prime }_i(t)-p_i(t)y_{i+1}(t)=0, \quad i=1,2,\dots , n-2, y^{\prime }_{n-1}(t)-p_{n-1}(t)|y_n(h_n(t))|^\alpha \mathop {\mathrm {s}gn}[y_n(h_n(t))]=0, y^{\prime }_n(t) \mathop {\mathrm {s}gn}[y_1(h_1(t))]+p_n(t)|y_1(h_1(t))|^\beta \, \le 0, \] where $ n\ge 3 $ is odd, $ \alpha >0$, $ \beta >0$.
LA - eng
KW - nonlinear differential system; oscillatory (nonoscillatory) solution; nonlinear differential system; oscillatory (nonoscillatory) solution
UR - http://eudml.org/doc/30942
ER -

References

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  1. On the oscillatory and monotone solutions of the first order differential equations with deviating arguments, J. Diff. Equations 8 (1982), 1463–1465. (Russian) (1982) 
  2. On the oscillatory behaviour of solution of system of differential equation with deviating arguments, Colloquia Math. Soc.  J. B., Qualitative theory of Diff. Eq. Szeged 30 (1979), 243–256. (1979) MR0680596
  3. On the oscillation of a class of nonlinear differential systems with deviating argument, J.  Math. Annal Appl. 66 (1978), 20–36. (1978) MR0513483
  4. On the oscillation of nonlinear differential systems with retarded arguments, Math. Slovaca 34 (1984), 73–88. (1984) MR0735938
  5. Functional Differential Equations, University of Žilina, EDIS, Žilina, 2000. (Slovak) (2000) 

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