Detail publikace

Positive solutions of nonlinear delayed differential equations with impulses

DIBLÍK, J.

Originální název

Positive solutions of nonlinear delayed differential equations with impulses

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

The paper is concerned with the long-term behavior of solutions to scalar nonlinear functional delayed differential equations $$\dot y(t)=-f(t,y_t),\,\,\,t\ge t_0. $$ It is assumed that $f\colon [t_0,\infty)\times {\cal C} \mapsto {\mathbb{R}}$ is a~continuous mapping satisfying a~local Lipschitz condition with respect to the second argument and ${\cal C}:={C}([-r,0],\mathbb{R})$, $r>0$ is the Banach space of conti\-nu\-ous functions. The problem is solved of the existence of positive solutions if the equation is subjected to impulses $y(t_s^+)=b_sy(t_s)$, $s=1,2,\dots$, where $t_0\le t_1< t_2<\dots$ and $b_s>0$, $s=1,2,\dots\,\,$. A criterion for the existence of positive solutions on $[t_0-r,\infty)$ is proved and their upper estimates are given. Relations to previous results are discussed as well.

Klíčová slova

Positive solution; large time behavior; delayed differential equation; impulse.

Autoři

DIBLÍK, J.

Vydáno

12. 4. 2017

Nakladatel

Elsevier

ISSN

0893-9659

Periodikum

APPLIED MATHEMATICS LETTERS

Ročník

72

Číslo

10

Stát

Spojené státy americké

Strany od

16

Strany do

22

Strany počet

7

URL

https://doi.org/10.1016/j.aml.2017.04.004

BibTex

@article{BUT137191,
  author="Josef {Diblík}",
  title="Positive solutions of nonlinear delayed differential equations with impulses",
  journal="APPLIED MATHEMATICS LETTERS",
  year="2017",
  volume="72",
  number="10",
  pages="16--22",
  doi="10.1016/j.aml.2017.04.004",
  issn="0893-9659",
  url="https://doi.org/10.1016/j.aml.2017.04.004"
}