THE CRITERION FOR SOLVABILITY OF A LINEAR NOETHER’S BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DYNAMICAL EQUATIONS ON A TIME SCALE
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 2
Abstract
On a time scale, the linear Noether’s boundary value problem for a system of second-order dynamical equations is considered. This boundary-value problem is considered in the case when the operator of the linear part is irreversible, that is, the number of boundary conditions of the problem and the order of the operator system are different. To establish the solvability conditions of the boundary-value problem under consideration, the apparatus of the theory of pseudo-inverse matrices is used. A connection is established between the condition of solvability of a dynamical system and the condition of solvability of an algebraic system of equations. That is, using the theory of pseudo-inverse matrices, the condition for solvability of a dynamical system of equations is established, which reduces the considered boundary value problem. In this case, the condition of solvability of a dynamical system of equations follows from the condition of solvability of the corresponding algebraic system of equations. A set of solutions of the boundary value problem under consideration is found. Also, partial cases of the boundary value problem are given, when the number of boundary conditions is greater than the number of unknowns of the system of dynamic equations and vice versa. For each of these cases, the solvability conditions of the boundary-value problem under consideration are found and its solutions are found. An example is provided illustrating the application of the results obtained.
Authors and Affiliations
T. V. Kovalchuk
Keywords
Related Articles
- EP ID EP558794
- DOI 10.18524/2519-206x.2018.2(32).149703
- Views 69
- Downloads 0
Some remarks on the absolute continuity of set-valued mappings
Recently, many authors have considered the existence, uniqueness and properties of solutions of set-valued differential and integral-differential equations, higher-order equations and investigated impulsive and control s...
To the theory of Hilbert space’s unconditional basis from values of entire vector-functions
Classes of entire functions of exponential type are considered in the article. They fulfil certain conditions related to theorems about unconditional basises from the values of entire vectorfunctions. In particular, for...
The rapid rotation of a dynamically asymmetric satellite in a gravitational field
We study the rapid rotary motion of the mass center of a dynamically asymmetric satellite in a gravitational field. The motion occurs in an elliptical orbit. A numerical study of the vector locus kinetic moment in three...
ON THE STRUCTURE OF THE FUNDAMENTAL MATRIX OF THE LINEAR HOMOGENEOUS DIFFERENRIAL SYSTEM OF THE SPECIAL KIND
For the linear homogeneous differenrial system, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, the kind of the fundamental matr...
On exponential sums involving the divisor function over Z[𝑖]
We apply the van der Corput transform to investigate the sums of view Σ︀ 𝑟(𝑛)𝑔(𝑛)𝑒(𝑓(𝑛))), where 𝑟(𝑛) is the number of representations of 𝑛 as the sum of two squares of integer numbers. Such sums have been studied by M....