A Model of Single Species Population Growth

Source abstract

The integral equation $$( * )\qquad x(t) = \int_0^L {P(L - s)h(t - L - \tau + s,x(t - L - \tau + s))} ds$$ can be viewed as a model of single species population growth as well as certain other biological or economic processes. Explicit bounds are determined for solutions of (*); these bounds are expressed in terms of the relative magnitude of $h(t,x)$, $\int _0^L P(L - s)ds$ and the norm of the initial function of the solution. These bounds are used to determine sufficient conditions for the existence of periodic solutions of (*).