On a linear system of differential equations

Abstract

The linear systems of partial differential equations of the first order with the identical main parts is considered. Аpplying the well-known relation between a normal system of ordinary differential equations and a linear system of partial differential equations of the first order with the same main parts, the existence of integral basis of a linear inhomogeneous system of partial differential equations of the first order adjoining to some solution of the same linear inhomogeneous system of differential equations with partial derivatives of the first order is proved. A sign at which the nonlinear system of ordinary differential equations has a neighborhood such that any solution with initial values from it tends to zero is found. Using the equivalence of a linear system of partial differential equations of the first order with identical main parts to a linear differential equation with partial derivatives of the first order, the existence of integral basis of the adjoining to zero linear homogeneous system of partial differential equations of first order with nonlinear coefficients is shown.

Keywords

• equation
• first order partial derivatives