Existence of positive periodic solutions for a periodic logistic equation
type: Item
instance of: scholarly article
title: Existence of positive periodic solutions for a periodic logistic equation
zbMATH Open document ID: 1031.45005
DOI: 10.1016/S0096-3003(02)00182-0
author: Guihong Fan
author: Yongkun Li
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: The paper deals with existence of \(\omega\)-periodic solutions for the following generalized logistic equations: \[ x'(t)=\pm x(t)\left[f\left(t, \int_{-r(t)}^{-\sigma(t)}x(t+s) d\mu(t,s)\right)-g(t, x(t-\tau(t, x(t))))\right], \] where \(\sigma,r\in C(\mathbb{R},(0,\infty))\) are \(\omega\)-periodic functions with \(\sigma(t)<r(t)\), \(f\), \(g\), \(\tau\), \(\mu\) \(\in C(\mathbb{R}\times\mathbb{R},\mathbb{R})\) are \(\omega\)-periodic functions with respect to their first variable and nondecreasing with respect to their second variable. Using the well known Mawhin's coincidence degree theorem [\textit{R. E. Gaines} and \textit{J. L. Mawhin}, Coincidence degree and nonlinear differential equations, Springer, Berlin (1977; Zbl 0339.47031), p. 40], the authors prove the existence of at least one positive \(\omega\)-periodic solution for each of the above equations.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45M15
zbMATH DE Number: 1978042
zbMATH Keywords: positive periodic solutions
zbMATH Keywords: logistic equation
zbMATH Keywords: coincidence degree
reviewed by: Panagiotis Ch. Tsamatos
MaRDI profile type: Publication
cites work: Delay differential equations: with applications in population dynamics
cites work: Ordinary differential equations with nonlinear boundary conditions
full work available at URL: s0096-3003(02)00182-0
OpenAlex ID: W2152047773
description: scientific article; zbMATH DE number 1978042