Four conjectures in Nonlinear Analysis

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.Comment: arXiv admin note: text overlap with arXiv:1504.01010, arXiv:1409.5919, arXiv:1612.0819