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
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topBačová, 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
top- On the oscillatory and monotone solutions of the first order differential equations with deviating arguments, J. Diff. Equations 8 (1982), 1463–1465. (Russian) (1982)
- 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
- On the oscillation of a class of nonlinear differential systems with deviating argument, J. Math. Annal Appl. 66 (1978), 20–36. (1978) MR0513483
- On the oscillation of nonlinear differential systems with retarded arguments, Math. Slovaca 34 (1984), 73–88. (1984) MR0735938
- Functional Differential Equations, University of Žilina, EDIS, Žilina, 2000. (Slovak) (2000)
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