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

• Main Author: Ermino, Marc Alvin R.
• Format: text
• Published: Animo Repository 2015
• Subjects: Differential equations, Partial; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/11308
• Institution: De La Salle University

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.