Ordinary differential equations, linear systems, linear equations, nonlinear systems, oscillation exponents, wandering exponents, rotation exponents.
Subject:
Qualitative theory of differential equations.
Biography
He defended his PhD thesis in 2013 in specialty 01.01.02. "Differential Equations, Dynamic Systems, and Optimal Control" on the topic "Some Properties of Solution Frequencies of Linear Differential Equations and Systems" (supervisor: Professor I.N. Sergeev).
He defended his doctoral thesis in 2024 in specialty 1.1.2. "Differential Equations and Mathematical Physics" on the topic "Indicators of Oscillation of Solutions of Linear Differential Equations and Systems" (advisor: Professor I.N. Sergeev).
Main publications:
Stash A.Kh., “Properties of complete and vector sign frequencies of
solutions of linear autonomous differential equations”, Differ. Equ., 50:10 (2014), 1413–1417
Stash A.Kh., “Existence of a two-dimensional linear system
with continual spectra of total and vector frequencies”, Differ. Equ., 51:1 (2015), 146–148
Stash A.Kh., “On the control of the spectra of upper strong
oscillation exponents of signs, zeros, and roots of third-order
differential equations”, Differ. Equ., 59:5 (2023), 597–605
Stash A.Kh., “Comparing the spectra of oscillation
exponents of a nonlinear system and the first approximation system”, Differ. Equ., 59:8 (2023), 1147–1150
Stash A.Kh., “On the properties of oscillation indices of solutions to differential systems”, Differ. Equ., 61:6 (2025), 769–824
A. E. Artisevich, A. Kh. Stash, “Realization of finite spectra of oscillation characteristics of linear homogeneous differential equations”, Mat. Zametki, 118:5 (2025), 643–653
2.
A. Kh. Stash, N. A. Loboda, “On the implementation of countable essential spectra of oscillation exponents in a linear homogeneous two-dimensional differential system”, Trudy Inst. Mat. i Mekh. UrO RAN, 31:1 (2025), 199–209
3.
A. Kh. Stash, A. E. Artisevich, “On some properties of the main values of the oscillation exponents of signs of linear differential equations of the third order”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 35:2 (2025), 282–296
A. Kh. Stash, “On some properties of strong oscillation exponents of solutions of linear homogeneous differential equations”, Vladikavkaz. Mat. Zh., 26:2 (2024), 122–132; 65, no. 6, 2024, 1475–1482
A. Kh. Stash, N. A. Loboda, “On the question of the residual of strong exponents of oscillation on the set of solutions of third-order differential equations”, Izv. Saratov Univ. Math. Mech. Inform., 23:3 (2023), 348–356
A. Kh. Stash, “On Essential Values of Oscillation Exponents for Solutions of a Linear Homogeneous Two-Dimensional Differential System”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:2 (2023), 157–171; Proc. Steklov Inst. Math., 321, suppl. 1 (2023), S216–S229
A. Kh. Stash, “Spectra of oscillation and rotatability exponents of solutions of homogeneous differential systems”, Vladikavkaz. Mat. Zh., 25:2 (2023), 136–143
A. Kh. Stash, A. E. Artisevich, “Existence of infinite everywhere discontinuous spectra of upper indicators in changes of signs, zeros and roots for third order differential equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 5, 16–22; Moscow University Mathematics Bulletin, 78:5 (2023), 223–229
A. Kh. Stash, “On the continuum spectra of the exponents of linear homogeneous differential systems”, Russian Universities Reports. Mathematics, 28:141 (2023), 60–67
A. Kh. Stash, “On essential values of Sergeev's frequencies and exponents of oscillation for solutions of a third-order linear differential periodic equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 141–155
A. Kh. Stash, “The absence of residual property for strong exponents of oscillation of linear systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 59–69
A. Kh. Stash, “Properties of exponents of oscillation of linear autonomous differential system solutions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 558–568
A. Kh. Stash, “The absence of residual property for total hyper-frequencies of solutions to third order differential equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 2, 65–68; Moscow University Mathematics Bulletin, 72:2 (2017), 81–83
A. Kh. Stash, “Spectra of total and vector frequencies of third-order linear differential equations”, Tr. Semim. im. I. G. Petrovskogo, 30 (2014), 252–269; J. Math. Sci. (N. Y.), 210:3 (2015), 270–280
