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

Abstract

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.