# differential equations

## On the question of the residual of strong exponents of oscillation on the set of solutions of third-order differential equations

In this paper, we study various types of exponents of oscillation (upper or lower, strong or weak) of non-strict signs, zeros, and roots of non-zero solutions of linear homogeneous differential equations of the third order with continuous and bounded coefficients on the positive semi-axis. A nonzero solution of a linear homogeneous equation cannot be zeroed due to the existence and uniqueness theorem. Therefore, the spectra of all the listed exponents of oscillation (i.e. their sets of values on nonzero solutions) consist of one zero value.

## On the application of the qualitative theory of differential equations to a problem of heat and mass transfer

The possibilities of applying the qualitative theory of differential equations to one problem of heat and mass transfer in multilayer planar semiconducting structures are studied. The consideration is carried out on the example of a mathematical model of a stationary process of diffusion of nonequilibrium minority charge carriers generated by a wide excitation source.

## On differential approximations of difference schemes

The concept of the first differential approximation was introduced in the 1950s for the analysis of difference schemes by A. I. Zhukov and then was used to study the quality of difference schemes approximating equations in partial derivatives. In the present work, the first differential approximation is considered as a universal construction that allows to use computer algebra methods for investigation difference schemes, bypassing the direct use of the methods of difference algebra.

## The research of some classes of almost periodic at infinity functions

The article under consideration is devoted to continuous almost periodic at infinity functions defined on the whole real axis and with their values in a complex Banach space. We consider different subspaces of functions vanishing at infinity, not necessarily tending to zero at infinity. We introduce the notions of slowly varying and almost periodic at infinity functions with respect to these subspaces. For almost periodic at infinity functions (with respect to a subspace) we give four different definitions.

## Solvability of Poisson's problem for Laplace operator on two dimensional stratified sets in usual sense

Solvability of Poisson's problem for Laplace operator on two dimensional stratified sets is established in usual sense.

## Solution of Cauchy Problem for Equation First Order Via Haar Functions

In this article we consider a Cauchy problem for the ﬁrst order differential equation and are looking for its numerical solution. For this aim we represent the derivative of the solution as Haar decomposition. We also obtain estimates of approximate solution. The method is computationally simple and applications are demonstrated through illustrative examples. These examples show that in some cases the error of the proposed method is much less, than in second order Runge – Kutta method.

## Application of Generalized Differential Quadrature Method to Two-dimensional Problems of Mechanics

The application of the generalized differential quadrature method to the solution of two-dimensional problems of solid mechanics is discussed by an example of the sample analysis of vibrations of a rectangular plate under various types of boundary conditions. The differential quadrature method (DQM) is known as an effective method for resolving differential equations, both ordinary and partial.