Publication detail

Increasing convergent and divergent solutions to nonlinear delayed differential equations

DIBLÍK, J. CHUPÁČ, R. RŮŽIČKOVÁ, M.

Original Title

Increasing convergent and divergent solutions to nonlinear delayed differential equations

English Title

Increasing convergent and divergent solutions to nonlinear delayed differential equations

Type

journal article in Web of Science

Language

en

Original Abstract

The paper is concerned with a nonlinear system of delayed differential equations as a generalization of an equation describing a simple model of the fluctuation of biological populations. The dependence of the behavior of monotone solutions on the coefficients and delays is studied and optimal sufficient conditions are derived for the existence of increasing and unbounded solutions and for the existence of increasing and convergent solutions. Inequalities estimating such solutions with some given increasing functions are derived as well. The results are compared with the linear case illustrated by examples, and open problems are formulated.

English abstract

The paper is concerned with a nonlinear system of delayed differential equations as a generalization of an equation describing a simple model of the fluctuation of biological populations. The dependence of the behavior of monotone solutions on the coefficients and delays is studied and optimal sufficient conditions are derived for the existence of increasing and unbounded solutions and for the existence of increasing and convergent solutions. Inequalities estimating such solutions with some given increasing functions are derived as well. The results are compared with the linear case illustrated by examples, and open problems are formulated.

Keywords

Delay; convergent solution; divergent solutions; monotone solution.

Released

01.09.2019

Publisher

Khayyam Publishing

Location

USA

ISBN

0893-4983

Periodical

Differential and Integral Equations

Year of study

32

Number

9-10

State

US

Pages from

493

Pages to

516

Pages count

24

URL

Documents

BibTex


@article{BUT158109,
  author="Josef {Diblík} and Radoslav {Chupáč} and Miroslava {Růžičková}",
  title="Increasing convergent and divergent solutions to nonlinear delayed differential equations",
  annote="The paper is concerned with a nonlinear system of delayed  differential equations as a generalization of an equation describing a simple model of the fluctuation of biological populations. The dependence of the behavior of monotone solutions on the coefficients and delays is studied and optimal sufficient conditions are derived for the existence of increasing and unbounded solutions and for the existence of increasing and convergent solutions. Inequalities estimating such solutions with some given increasing functions are derived as well. The results are compared with the linear case illustrated by examples, and open problems are formulated.",
  address="Khayyam Publishing",
  chapter="158109",
  institution="Khayyam Publishing",
  number="9-10",
  volume="32",
  year="2019",
  month="september",
  pages="493--516",
  publisher="Khayyam Publishing",
  type="journal article in Web of Science"
}