Detail publikace

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

OPLUŠTIL, Z.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

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).

Klíčová slova

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

Autoři

OPLUŠTIL, Z.

Vydáno

18. 7. 2018

ISSN

1787-2413

Periodikum

Miskolc Mathematical Notes (electronic version)

Ročník

19

Číslo

1

Stát

Maďarsko

Strany od

439

Strany do

459

Strany počet

21

BibTex

@article{BUT149261,
  author="Zdeněk {Opluštil}",
  title="Oscillatory properties of certain system of non-linear ordinary differential equations",
  journal="Miskolc Mathematical Notes (electronic version)",
  year="2018",
  volume="19",
  number="1",
  pages="439--459",
  doi="10.18514/MMN.2018.2391",
  issn="1787-2413"
}