# Four conjectures in Nonlinear Analysis

## TL;DR

This paper presents four challenging conjectures in Nonlinear Analysis, covering topics like the Monge-Ampère equation, eigenvalue problems, non-local problems, and solution connectedness, aiming to stimulate further research in these areas.

## Contribution

It introduces four new conjectures in Nonlinear Analysis, highlighting open problems and potential directions for future mathematical investigation.

## Key findings

- Formulation of a conjecture on the Monge-Ampère equation
- Proposal of a conjecture on an eigenvalue problem
- Introduction of a conjecture on disconnectedness versus infinitely many solutions

## Abstract

In this chapter, I formulate four challenging conjectures in Nonlinear Analysis. More precisely: a conjecture on the Monge-Amp\`ere equation; a conjecture on an eigenvalue problem; a conjecture on a non-local problem; a conjecture on disconnectedness versus infinitely many solutions.