Generalized solutions of nonlinear differential equations A nonstandard jets approach

TL;DR

This paper employs nonstandard jets theory to extend existence results for generalized solutions from linear to a broad class of nonlinear differential equations, advancing the mathematical framework for solving complex PDEs.

Contribution

It introduces a nonstandard jets approach to broaden the scope of existence results for generalized solutions of nonlinear differential equations.

Findings

Extended existence results to nonlinear PDEs

Deepened understanding of nonstandard jets in PDE theory

Broader class of nonlinear equations addressed

Abstract

Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear differential equations to a much broader class of nonlinear differential equations.