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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 1, 2004, pp. 3–15
DOI: 10.4171/ZAA/1185

Published online: 2004-03-31

A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I

Lothar von Wolfersdorf

By means of the iteration method with weighted norms existence and uniqueness theorems are proved for three classes of nonlinear integral equations and first order integro-differential equations in two variables. The quadratic non-linearity is given by the correlation-convolution integral. Existence and uniqueness of the solutions are shown in Lebesgue spaces with mixed norms in rectangle and strip.

Keywords: Nonlinear integral equation, nonlinear partial integro-differential equations, correlation-convolution integral, iteration method with weighted norms

von Wolfersdorf Lothar: A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I. Z. Anal. Anwend. 23 (2004), 3-15. doi: 10.4171/ZAA/1185