TY  - JOUR
T1  - On the Behavior of Solutions of a Fourth-Order Differential System at Infinity
AU - Berdenova, G.Zh. AU - Zhikeyev, A.A. AU - Utemissova, A.A. 
JO  - Journal of Engineering and Applied Sciences
VL  - 14
IS  - 3
SP  - 725
EP  - 733
PY  - 2019
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2019.725.733
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2019.725.733
KW  - elements
KW  -asymptotic behavior
KW  -L-diagonal system
KW  -system of differential equations
KW  -Fundamental system of solutions
KW  -symmetricmatrix
KW  -uniformly with respect to x
AB  - The asymptotic behavior of the fundamental system of solutions of two fourth-order singular
differential equations for large values of the spectral parameter is investigated in this article. The asymptotic
formulas for the fundamental system of solutions are determined uniformly with respect to x when ly = λy, λ∈Γ,
λ→∞ in the case of slow rotation of the eigenvectors of the real symmetric matrix Q(x) with twice continuously
differentiable elements. Replacing the variables in the system of equations of the fourth order allows us to pass
to a system of equations of the first order with a new unknown vector function. An orthogonal matrix is
introduced which can be reduced to diagonal form by means of transformations. For the system of equations
in the space of vector-functions, asymptotic formulas are obtained and proved. Due to the uniformity of the
asymptotic formulas, the asymptotics of the spectrum of the corresponding differential operator is calculated
in this study. Using the obtained formulas, the defect indices of the corresponding differential operators are
calculated.
ER  -