Про деякі підходи до розв’язання нелінійної еліптичної крайової задачі в областях складної геометрії

Abstract

The paper deals with the question of the existence, uniqueness and the possibility of constructing successive approximations to the solution of one problem on the choice of population migration model in genetics, the mathematical model of which is the Dirichlet boundary value problem for a nonlinear elliptic equation. To solve this problem, the Green's quasifunction method is used, which allows one to find approximate solutions. Conditions are obtained that must satisfy the parameters included in the statement of the problem so that it is possible to construct successive approximations to a positive solution.