Petropoulou, Eugenia N. Existence and uniqueness of analytic solutions of the Shabat equation. (English) Zbl 1113.34062 Abstr. Appl. Anal. 2005, No. 8, 855-862 (2005). The author presents sufficient conditions, so that the initial value problem for the Shabat equation has a unique analytic solution, which together with its first derivative, converges absolutely for \(z\in\mathbb{C}: |z|<T\), \(T> 0\). The basic idea of the method is the equivalent transformation of the functional differential equation under consideration into an operator equation. Reviewer: S. D. Bajpai (Indore) Cited in 1 Document MSC: 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain Keywords:analytic solution; Shabat equation; Hilbert space PDFBibTeX XMLCite \textit{E. N. Petropoulou}, Abstr. Appl. Anal. 2005, No. 8, 855--862 (2005; Zbl 1113.34062) Full Text: DOI EuDML