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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 5, 1984, pp. 385–399
DOI: 10.4171/ZAA/116

Published online: 1984-10-31

On Strongly Nonlinear Poincaré Boundary Value Problems for Harmonic Functions

Lothar von Wolfersdorf

A class of strongly nonlinear Poincaré problems for harmonic functions in the unit disk is studied by reducing them to a new integral equation system to which Schauder’s fixed point theorem is applied. Specific existence results are given for several special cases, in particular the quasilinear case is dealt with in detail.

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von Wolfersdorf Lothar: On Strongly Nonlinear Poincaré Boundary Value Problems for Harmonic Functions. Z. Anal. Anwend. 3 (1984), 385-399. doi: 10.4171/ZAA/116