The Cauchy-Kowalewski theorem in the space of pseudo Q-holomorphic functions

Abstract

In this work, we prove the Cauchy-Kowalewski theorem for the initial-value problem where partial derivative w/partial derivative t = Lw w(0, z) = w(0)(z) Where Lw : E-0(t, z) partial derivative/partial derivative(phi) over bar (E-d(w)/dz) + F-0(t, z) <((partial derivative/partial derivative<(phi)over bar>(E-d(w)/dz))over bar> + C-0(t, z) E-d(w)/dz +G(0)(t, z) (E-d(w)/dz) + A(0)(t, z)w + B-0(t, z)(w) over bar + D-0(t, z) in the space P-D (E) of Pseudo Q-holomorphic functions.