The analytic Schwarz kernel function the real part of which is the harmonic Poisson kernel was generalized to a polyanalytic Schwarz kernel in a joint work with G. N. Hile [Rocky Mountain J. Math. 27 (1997) 669--706], see also H. Begehr [Complex Analytic Methods for Partial Differential Equations. An Introductory Text, Singapore: World Scientific 1994]. It is here used to give some higher order Cauchy-Schwarz-Pompeiu representations and to solve the Schwarz problem for the Poisson, the inhomogeneous Bitsadze and the inhomogeneous polyanalytic equation.