Solvability analysis of the nonlinear integral equations system arising in the logistic dynamics model in the piecewise constant kernels case

The work is devoted to the analysis of a nonlinear integral equation that arises as a result of parametric closure of the third spatial moment in a single-species model of logistic dynamics by U. Dieckmann and R. Law. The case of piecewise constant kernels is analyzed, which is very important for further computer modeling. Sufficient conditions have been found to guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels made it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates were obtained for the norm of the solution, as well as for the closure parameter.