Detail publikace

# Oscillatory properties of certain system of non-linear ordinary differential equations

Originální název

Oscillatory properties of certain system of non-linear ordinary differential equations

Anglický název

Oscillatory properties of certain system of non-linear ordinary differential equations

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).

BibTex

``````
@article{BUT149261,
author="Zdeněk {Opluštil}",
title="Oscillatory properties of certain system of non-linear ordinary differential equations",
annote="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).",
chapter="149261",
doi="10.18514/MMN.2018.2391",
howpublished="online",
number="1",
volume="19",
year="2018",
month="july",
pages="439--459",
type="journal article in Web of Science"
}``````