Detail publikace
Oscillatory properties of certain system of non-linear ordinary differential equations
OPLUŠTIL, Z.
Anglický název
Oscillatory properties of certain system of non-linear ordinary differential equations
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
We consider certain two-dimensional system of non-linear differential equations u'=g(t)|v|^(1/A)sgn v v'=-p(t)|u|^(A) sgn u, where A is a positive number, g,p are locally integrable functions (g is non-negative). In the case when coefficient g is not inegrable on the half-line, the considered system has been widely studied in particular cases such linear systems as well as second order linear and half-linear differential equations. However, the case when function g is integrable on the hlaf-line has not been studied in detail in the existing literature. Moreover, we allow that the coefficient g can have zero points in any neigh- bourhood of in finity and consequently, considered system can not be rewritten as the second order linear or half-linear differential equation in this case. In the paper, new oscillation criteria are established in the case when function g is integrable on the hlaf-line and without restricted assumption function p preserves its sign (which is usually considered).
Anglický abstrakt
We consider certain two-dimensional system of non-linear differential equations u'=g(t)|v|^(1/A)sgn v v'=-p(t)|u|^(A) sgn u, where A is a positive number, g,p are locally integrable functions (g is non-negative). In the case when coefficient g is not inegrable on the half-line, the considered system has been widely studied in particular cases such linear systems as well as second order linear and half-linear differential equations. However, the case when function g is integrable on the hlaf-line has not been studied in detail in the existing literature. Moreover, we allow that the coefficient g can have zero points in any neigh- bourhood of in finity and consequently, considered system can not be rewritten as the second order linear or half-linear differential equation in this case. In the paper, new oscillation criteria are established in the case when function g is integrable on the hlaf-line and without restricted assumption function p preserves its sign (which is usually considered).
Klíčová slova anglicky
Two-dimensional system of non-linear differential equations; oscillatory criteria, half-linear differential equation
Vydáno
18.07.2018
ISSN
1787-2413
Ročník
19
Číslo
1
Strany od–do
439–459
Počet stran
21
BIBTEX
@article{BUT149261,
author="Zdeněk {Opluštil},
title="Oscillatory properties of certain system of non-linear ordinary differential equations",
year="2018",
volume="19",
number="1",
month="July",
pages="439--459",
issn="1787-2413"
}