Application of the Leray-Schauder Principle to the Analysis of a Nonlinear Integral Equation
We study a nonlinear integral equation arising from the parametric closure for the third spatial moment in the Dieckmann-Law model of stationary biological communities. The existence of a fixed point of the integral operator defined by this equation is analyzed. The noncompactness of the resulting operator is proved. Conditions are stated under which the equation in question has a nontrivial solution.