The ordinary differential equations systems solubility in respect to the derivatives
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 2
Abstract
Questions are investigated about bringing the system of ordinary differential equations not solved with respect to derivatives to the systems, solved with respect to derivatives, or partially solved with respect to derivatives.
Authors and Affiliations
I. Chernetska
THE CRITERION FOR SOLVABILITY OF A LINEAR NOETHER’S BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DYNAMICAL EQUATIONS ON A TIME SCALE
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 i...
Split of gas stream onto the bubbles inside liquid
A theory of the approximate description of the splitting of the thin jat of ideal gas flowing into the incompressible frictionless liquid is constructed on the base of the balance equations of mass and energy. Under the...
Approximation of classes of Poisson integrals by 𝑟-repeated de la Vallee Poussin sums
We obtain asymptotic formulas for upper bounds of the deviations of trigonometric polynomials, generated by repeated de la Vallee Poussin methods of summation, taken over classes of Poisson integrals.
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...
Estimates of the norms of Riesz derivatives of multivariate functions
Let Δ = 𝜕2 𝜕𝑥1 + ... + 𝜕2 𝜕𝑥𝑚 be the Laplace operator. We denote by 𝐿𝑠(R𝑚) (1 6 𝑠 6 ∞) the spaces of measurable functions 𝑓 : R𝑚 → R with a finite norm ‖𝑓‖𝑠. Let 𝐹 and 𝐸 be ideal lattices on R𝑚 with finite norms ‖ ・ ‖𝐹...