Title :

Étude analytique de l'équation pantographe au moyen de fonctions thêta de Jacobi

Author(s) :

Zhang, Changgui [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Mathematics Subject Classification 2010: 34K06 34M40 33E30 pantograph equation q-difference equation connection problem Jacobi θ-function
Mathematics Subject Classification 2010: 34K06
34M40
33E30 pantograph equation
q-difference equation
connection problem
Jacobi θ-function

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

The aim of this paper is to use the analytic theory of linear qdifference equations for the study of the functional-differential equation y ′ (x) = ay(qx)+by(x), where a and b are two non zero real or complex numbers. When ...
Show more >The aim of this paper is to use the analytic theory of linear qdifference equations for the study of the functional-differential equation y ′ (x) = ay(qx)+by(x), where a and b are two non zero real or complex numbers. When 0 < q < 1 and y(0) = 1, the associated Cauchy problem admits a unique power series solution, n≥0 (−a/b; q)n n! (bx) n , that converges in the whole complex xplane. The principal result obtained in the paper explains how to express this entire function solution into a linear combination of solutions at infinity, with the help of integral representaions involving Jacobi theta functions. As a by-product, this connection formula between zero and infinity allows one to rediscover a classic Theorem of Kato and McLeod on the asymptotic behavior of the solutions over the real axis.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL