Iterative method for solving a nonlinear Robin problem

TL;DR

This paper introduces an iterative approach to solve a nonlinear elliptic Robin boundary value problem in 2, establishing existence and uniqueness of solutions under certain boundary conditions.

Contribution

It extends previous linear Robin problem studies to nonlinear cases, providing a new iterative method for existence and uniqueness proofs.

Findings

Proves existence of solutions for the nonlinear Robin problem.

Establishes uniqueness of solutions under admissible boundary conditions.

Develops an iterative construction method for solving the nonlinear problem.

Abstract

In \cite{CJ1} M. Jaoua et al. studied the linear approximation of Robin problem on $\Omega$ an open bounded domain of $\R^d$, and they given some important results. In this paper, we study a nonlinear approximation of an elliptic problem with a nonlinear Robin boundary condition in a domain of $\R^2$. We prove the existence and uniqueness of solution by an iterative construction method with admissible condition on $\partial\Omega$.