Positive solutions of nonlinear integral equations and surjectivity of Non-Linear Markov Operators On Infinite Dimensional Simplex

TL;DR

This paper investigates the existence of positive solutions for nonlinear integral equations by analyzing the surjectivity of nonlinear Markov operators on infinite-dimensional simplexes.

Contribution

It provides necessary and sufficient conditions for the surjectivity of nonlinear Markov operators, advancing understanding of their role in solving nonlinear integral equations.

Findings

Established criteria for surjectivity of nonlinear Markov operators.

Connected surjectivity to the existence of positive solutions of integral equations.

Enhanced theoretical framework for nonlinear integral equations and Markov operators.

Abstract

In the present paper, we consider the solvability of positive solutions of nonlinear integral equations by means of investigating non-linear Markov operators. To solve the problem we find necessary and sufficient condition for the surjectivity of nonlinear Markov operators.