Existence and uniqueness of analytic solutions of the Shabat equation

Eugenia N. Petropoulou

Abstract and Applied Analysis, 2005, vol. 2005, 1-8

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 ∈ ℂ : | 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:284895

DOI: 10.1155/AAA.2005.855

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