On the solvability of a system involving a singular equation of Gerard-Tahara type of partial differential equation

College

College of Science

Document Type

Archival Material/Manuscript

First Page

1

Last Page

24

Publication Date

2015

Abstract

This paper investigates the existence and uniqueness of holomorphic solutions of par- tial differential equations of Gerard-Tahara type. Such equations are PDE generalizations of the Briot-Bouquet type ordinary differential equation studied by Briot and Bouquet in the late 1800s. More particularly, this paper presents the higher order extensions of the Gerard-Tahara type PDE and of a system of PDEs studied by Bielawki. The proofs make use of a fundamental lemma attributed to Nagumo in estimating spatial derivatives and of the Implicit Function Theorem in proving the existence of a function that majorizes the unique formal solution.

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Disciplines

Mathematics

Keywords

Differential equations, Partial

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