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Jul 12, 2022Open Access
With the help of Mindlin’s tensor, the problem of heterogeneity in an elastic halfspace comes down to the solution system of integrable equations. Different versions of the solution of such systems are considered. The main attention is paid to the solution of integrable equations with small parameters.
Feb 24, 2021Open Access
If to apply bidimensional Fourier’s transform to homogeneous system of equations of the theory of elasticity, then we will receive system of ordinary differential equations. The general solution of this system contains 6 arbitrary constants and allows to solve problems for the layer and the multilayer environment. It is shown that it is convenient to do statement and the solution of such tasks in the matrix form. The task for the layer on the elastic halfspace is solved. Ways of inverse of Four...
May 07, 2020Open Access
The purpose of this paper is to study the stability of nonlinear fractional Duffing equation where , by analysing the eigenvalues generated from the system of the given differential equation. Graphical results furthermore show the effect of the damping and nonlinear parameter on the system. Our contribution relies on its application to the choice of hard/soft spring in the mechanism of shock absorbers.
Mar 23, 2020Open Access
The main aim in this work is to obtain an integral inequality with a clear estimate on time scales. The obtained inequality is used as a tool to investigate some basic qualitative properties of solutions to certain nonlinear VolterraFredholm integrodifferential equations on time scales.
Feb 13, 2020Open Access
The analog of the quadrature solution of the equation of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Equations of Fredholm and Volterra are considered. The graphical representation of the solution is discussed. Computing examples show expediency of such approach in appropriate cases.
Sep 12, 2019Open Access
The analog of the quadrature solution of the equation of Fredholm of the second kind is considered. Fundamental difference from classical quadrature formulas is as follows. On segments of the chosen grid not values of functions, but their integral average values are used. Computing examples show expediency of such approach in appropriate cases.
Aug 29, 2019Open Access
For importance of the trigonometric integrals, we have in this paper finding a series of power, some of trigonometric functions that did not exist before in the first section. As shown in the Section two, where, the integration of trigonometric function with power n has been achieved and approved, this result is considered as the first achievement. while in the third section we find integrals ...
Dec 15, 2017Open Access
This paper is concerned with the construction of a class of polynomial orthogonal with respect to the weight function w(x)=1x^{2} over the interval [0,1]. The zeros of these polynomials were employed as points of co ...
Dec 22, 2014Open Access
This paper investigated oscillatory properties of solutions for nonlinear
parabolic equations with impulsive effects under two different boundary
conditions. By using integral averaging method, variable substitution and
functional differential inequalities, we established several sufficient
conditions. At last, we provided two examples to illustrate the results.
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