On the Fixed Point Principle for Matrix Partial Differential Systems of Fedorov-Riccati Type

Abstract

For a general first-order linear normal partial differential system, an invariant Banach space in which the integral operator L of the corresponding Cauchy problem satisfies the condition |||L||| < 1 was constructed in [1] on the basis of the majorant method. Thus the Cauchy–Kowalewski theorem can be proved for linear equations on the basis of the classical Banach–Caccioppoli fixed point principle without resorting to a scale of Banach spaces [2, 3]. In the present paper, we generalize this result to matrix partial differential systems.