Improving the G. E. Hutchinson Population Model for Functional-Differential Equations

Abstract:

The article is devoted to improve the G. E. Hutchinson population model for functio-nal-differential equations. The functional-differential equation with maxima is considered under the boundary conditions. The issues of unique classical solvability and construction of a solution to a boundary problem for a nonhomogeneous functional- differential equation containing maxima of unknown function are studied. The proposed functional-differential equation with maxima is considered as a mathematical model of population dynamics of a species. Sufficient coefficient conditions for unique classical solvability of the boundary problem are established. The method of successive approx- imations is used with combination of the contracting mapping method. The examples with illustrations of the properties of solution of the functional-differential equation with maxima are given.