Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2004-03-31
A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral ILothar 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