Analytical Investigation of Positive Continuous Solutions for Nonlinear Quadratic Integral Equations of Hammerstein Type via Fixed-Point Methodological Approaches

Abstract

This study establishes rigorous existence criteria for positive continuous solutions to a significant class of nonlinear quadratic integral equations of Hammerstein type. The investigation employs Schauder's fixed-point theorem as the principal analytical tool to derive the main existence result. Furthermore, under appropriately formulated monotonicity constraints, the existence of both maximal and minimal solutions is demonstrated. These theoretical contributions extend the existing mathematical literature on quadratic integral equations by introducing novel methodological frameworks and broadening the domain of applicability for this important category of nonlinear functional equations.