Detail publikačního výsledku

Positive solutions of nonlinear delayed differential equations with impulses

DIBLÍK, J.

Originální název

Positive solutions of nonlinear delayed differential equations with impulses

Anglický název

Positive solutions of nonlinear delayed differential equations with impulses

Druh

Článek WoS

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.

Anglický 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.

Klíčová slova v angličtině

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

Autoři

DIBLÍK, J.

Rok RIV

2018

Vydáno

12.04.2017

Nakladatel

Elsevier

ISSN

0893-9659

Periodikum

Applied Mathematics Letters

Svazek

72

Číslo

10

Stát

Spojené státy americké

Strany od

16

Strany do

22

Strany počet

7

URL

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"
}