Polynomial solutions of nonlinear integral equations

TL;DR

This paper investigates polynomial solutions to nonlinear integral equations, extending previous work, and identifies conditions under which orthogonal solutions exist, providing their general form via kernel polynomials.

Contribution

It generalizes earlier research by analyzing conditions for polynomial and orthogonal solutions in nonlinear integral equations, offering explicit forms using kernel polynomials.

Findings

Orthogonal polynomial solutions can exist under certain conditions.

The general form of solutions is expressed through kernel polynomials.

Extension of previous work by Bender and Ben-Naim on polynomial solutions.

Abstract

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.