Differential and Integral Equations

Increasing convergent and divergent solutions to nonlinear delayed differential equations

Radoslav Chupáč, Josef Diblík, and Miroslava Růžičková

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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.

Article information

Source
Differential Integral Equations, Volume 32, Number 9/10 (2019), 493-516.

Dates
First available in Project Euclid: 13 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1565661619

Mathematical Reviews number (MathSciNet)
MR3992035

Subjects
Primary: 34K12: Growth, boundedness, comparison of solutions 92D25: Population dynamics (general)

Citation

Diblík, Josef; Chupáč, Radoslav; Růžičková, Miroslava. Increasing convergent and divergent solutions to nonlinear delayed differential equations. Differential Integral Equations 32 (2019), no. 9/10, 493--516. https://projecteuclid.org/euclid.die/1565661619


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