On Picard Type Theorems and Entire Solutions of Differential Equations

TL;DR

This paper explores the relationship between Picard type theorems and entire solutions of differential equations, extending classical results to higher dimensions and providing new insights into both ordinary and partial differential equations.

Contribution

It establishes a novel connection between Picard theorems and the characterization of entire solutions, including higher-dimensional generalizations.

Findings

New characterizations of entire solutions of differential equations.

Extensions of Picard type theorems to higher dimensions.

Implications for both ordinary and partial differential equations.

Abstract

We give a connection between the Picard type theorem of Polya-Saxer-Milliox and characterization of entire solutions of a differential equation and then their higher dimensional extensions, which leads further results on both (ordinary and partial) differential equations and Picard type theorems.