TY - JOUR
AU - Aldibekov, T. М.
AU - Aldazharova, M. M.
PY - 2019/04/23
Y2 - 2024/11/06
TI - On a linear system of differential equations
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 101
IS - 1
SE - Mathematics
DO - 10.26577/JMMCS-2019-1-615
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/615
SP - 3-13
AB - <p>The linear systems of partial differential equations of the first order with the identical main parts<br>is considered. Аpplying the well-known relation between a normal system of ordinary differential<br>equations and a linear system of partial differential equations of the first order with the same<br>main parts, the existence of integral basis of a linear inhomogeneous system of partial differential<br>equations of the first order adjoining to some solution of the same linear inhomogeneous system<br>of differential equations with partial derivatives of the first order is proved. A sign at which the<br>nonlinear system of ordinary differential equations has a neighborhood such that any solution with<br>initial values from it tends to zero is found. Using the equivalence of a linear system of partial<br>differential equations of the first order with identical main parts to a linear differential equation<br>with partial derivatives of the first order, the existence of integral basis of the adjoining to zero<br>linear homogeneous system of partial differential equations of first order with nonlinear coefficients<br>is shown.</p>
ER -