Publication detail

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

OPLUŠTIL, Z.

English title

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

Type

journal article in Web of Science

Language

en

Original abstract

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).

English abstract

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).

Keywords in English

Two-dimensional system of non-linear differential equations; oscillatory criteria, half-linear differential equation

Released

18.07.2018

ISSN

1787-2413

Volume

19

Number

1

Pages from–to

439–459

Pages count

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"
}