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-T))/K), dt (1.1) where Y, z, c, K are assumed to be positive constants. This equation is a natural generalization of the well-known elementary logistic equation which has been used as a model for single species population growth, i(t)=rx(t)(l-x(t)/K), (1.2) where r is the intrinsic growth rate of species x and K is interpreted as the environment capacity for x. In [ll, pp. 38401, F. E. Smith argued that per capita growth rate r(1-x(t)/K) in (1.2) should be replaced by r(1-(x(t) + ci(t))/K), based on his investigation on laboratory populations of Daphnia magna. Obviously, it will be even more realistic to incor