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16 October 2005 Existence and uniqueness of analytic solutions of the Shabat equation
Eugenia N. Petropoulou
Abstr. Appl. Anal. 2005(8): 855-862 (16 October 2005). DOI: 10.1155/AAA.2005.855

Abstract

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for z:|z|<T, T>0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and T. Furthermore, from these conditions, one can obtain an upper bound for T. Our results are in consistence with some recently found results.

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Eugenia N. Petropoulou. "Existence and uniqueness of analytic solutions of the Shabat equation." Abstr. Appl. Anal. 2005 (8) 855 - 862, 16 October 2005. https://doi.org/10.1155/AAA.2005.855

Information

Published: 16 October 2005
First available in Project Euclid: 22 December 2005

zbMATH: 1113.34062
MathSciNet: MR2201920
Digital Object Identifier: 10.1155/AAA.2005.855

Rights: Copyright © 2005 Hindawi

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