Application of a Generalized Fixed Point Principle to the Study of a System of Nonlinear Integral Equations Arising in the Population Dynamics Model

The paper deals with the analysis of a system of nonlinear integral equations resulting from the three-parameter closure of the third spatial moment in the Dieckmann–Law model in the case of an -species community in an -dimensional space. For the analysis of its solvability, this system is represented as an operator equation in a Banach space of a special form. Sufficient conditions for the existence of a nontrivial solution are stated using a generalized fixed point principle.