On the solvability of some systems of quadratic integral equations in dimensions two and three

TL;DR

This paper investigates the existence of solutions for specific systems of quadratic integral equations in two and three dimensions, using fixed point methods to establish the presence of solutions under perturbations.

Contribution

It introduces a fixed point approach to prove the existence of solutions for quadratic integral systems in low-dimensional spaces, extending previous results.

Findings

Existence of solutions established for quadratic integral systems in 2D and 3D.

Application of fixed point techniques to nonlinear integral equations.

Results applicable to systems in H^2(R^d, R^N) spaces.

Abstract

The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.