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.
Cite this article
Lothar von Wolfersdorf, A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I. Z. Anal. Anwend. 23 (2004), no. 1, pp. 3–15DOI 10.4171/ZAA/1185