Improving the G. E. Hutchinson Population Model for Functional-Differential Equations
Annotatsiya
The article is devoted to improve the G. E. Hutchinson population model for functional-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 approximations 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.