On Solvability of a Class of Multidimensional Integral Equations in the Mathematical Theory of Geographic Distribution of an Epidemic

摘要

A multidimensional convolution-type integral equations with concave nonlinearity is investigated. This equation arises in the mathematical theory of the geographic distribution of an epidemic. The combination of well-known multidimensional methods and operator methods for constructing invariant cone segments for such operators with methods of the theory of convolution-type integral operators and limit theorems of the function theory allow proving the existence of positive bounded solutions to such equations. The asymptotic behavior of the constructed solutions is also studied. In a specific cone segment, the uniqueness of the solution is also proved. Particular applied examples of these equations are given.