Application of the Leray-Schauder Principle to the Analysis of a Nonlinear Integral Equation
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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.
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The authors express their gratitude to Ulf Dieckmann for posing this problem and for his interest in this work.
A.A. Nikitin’s research was supported by Russian Science Foundation, project no. 17-11-01168.
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