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DIBLÍK, J.
Original Title
Positive solutions of nonlinear delayed differential equations with impulses
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
Positive solution; large time behavior; delayed differential equation; impulse.
Authors
Released
12. 4. 2017
Publisher
Elsevier
ISBN
0893-9659
Periodical
APPLIED MATHEMATICS LETTERS
Year of study
72
Number
10
State
United States of America
Pages from
16
Pages to
22
Pages count
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" }