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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 3, 1992, pp. 377–384
DOI: 10.4171/ZAA/599

Published online: 1992-09-30

A Note on the Existence and Uniqueness of Holder Solutions of Nonlinear Singular Integral Equations

Jürgen Appell[1], Antonio Carbone[2] and Petr P. Zabrejko[3]

(1) Universität Würzburg, Germany
(2) Università della Calabria, Arcavacata Di Rende, Italy
(3) Belgos University, Minsk, Belarus

The purpose of this note is to apply a generalized Kantorovich majorization principle to existence and uniqueness results for Hölder solutions of nonlinear singular integral equations. In contrast to the classical Kantorovich priziciple, we do notrequire differentiability, but only a local Lipschitz condition.

Keywords: Nonlinear singular integral equations, Hölder solutions, local Lipschitz condition, Kantorovich mojorization principle, Banach-Caccioppoli principle

Appell Jürgen, Carbone Antonio, Zabrejko Petr: A Note on the Existence and Uniqueness of Holder Solutions of Nonlinear Singular Integral Equations. Z. Anal. Anwend. 11 (1992), 377-384. doi: 10.4171/ZAA/599