Oscillation of a logistic equation with delay and diffusion

On Oscillation of a Generalized Logistic Equation with Several Delays

Oscillation of a Logistic Difference Equation with Several Delays

Difference equations provide an important framework for analysis of dynamical phenomena in biology, ecology, economics, and so forth. For example, in population dynamics discrete systems adequately describe organisms for which births occur in regular, usually short, breeding seasons. Recently the problem of oscillation and nonoscillation of solutions for nonlinear delay difference equations has...

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

Delay differential logistic equation with harvesting

l~(t) = r(t)N(t) a bkN(hk(t)) cz(t)N(gl(t)), t >_ O, l = l N(t )=~( t ) , t<O, N(O)=No, is considered. The existence and the bounds of positive solutions are studied. Sufficient conditions for the extinction of the solution are presented. © 2005 Elsevier Ltd. All rights reserved. K e y w o r d s D e l a y logistic equations, Linear harvesting, Positive solutions, Extinction of the population, S...

A Logistic Equation with Refuge and Nonlocal Diffusion

In this work we consider the nonlocal stationary nonlinear problem (J ∗ u)(x) − u(x) = −λu(x) + a(x)u(x) in a domain Ω, with the Dirichlet boundary condition u = 0 in R \ Ω and p > 1. The kernel J involved in the convolution (J ∗ u)(x) = RN J(x− y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed t...