Oscillation and nonoscillation in a nonautonomous delay-logistic equation

Oscillation and Nonoscillation of Even - Order Nonlinear Delay - Differential Equations

for their oscillatory and nonoscillatory nature. In Eqs. (1) and (2) y("(x) = (d%/dx')y{x), i = 1, 2, • • • , 2n; yr(x) = y(x — t(x))] dy/dx and d2y/dx2 will also be denoted by y' and y" respectively. Throughout this paper it will be assumed that p(x), j(x), t{x) are continuous real-valued functions on the real line (—°°, °°); j(x), p(x) and t(x), in addition, are nonnegative, r(x) is bounded a...

Global Attractivity and Oscillations in a Periodic Delay - Logistic Equation

in which r and K are positive numbers; r is related to the reproduction of the species while K is related to the capacity of the environment to sustain the population. It is assumed that there is no immigration or emigration and other characteristics such as age dependence and interactions with other species are assumed to be not significant. Elementary analysis of (1.1) indicates that the solu...

Qualitative Analysis of a Nonautonomous Nonlinear Delay Differential Equation

This paper is devoted to the systematic study of some qualitative properties of solutions of a nonautonomous nonlinear delay equation, which can be utilized to model single population growths. Various results on the boundedness and oscillatory behavior of solutions are presented. A detailed analysis of the global existence of periodic solutions for the corresponding autonomous nonlinear delay e...

Boundedness of Solutions of a Nonlinear Nonautonomous Neutral Delay Equation

Sufficient conditions are obtained for the boundedness of solutions of the non-linear nonautonomous neutral equation i(t)=r(f)x(t)(a(f)-.x(t-1)-c(/).?(t-1)), which arise in a " food-limited " population model. This partially answers a recent open question proposed The nonlinear neutral delay logistic equation was first introduced and extensively discussed in [6], dx(t)-=i(t)=rx(t)(l-(x(t-)+ci(t...

On Oscillation of a Generalized Logistic Equation with Several Delays