Nonaxisymmetric boundary value problem of elasticity theory for multiconnected body with cylindrical boundaries is investigated. The solution is constructed as a superposition of basic solutions of the Lame equation in coordinate systems related to the centers of body boundary surfaces. Boundary conditions are satisfied exactly by the generalized Fourier method. The numerical analysis of stresses in the areas of their greatest concentration is carried out.

Keywords: multiconnected body, cylindrical boundaries, generalized Fourier method, stress concentration.

The justification of the method for numerical solution of the boundary integral equations of the problems of waves scattering of on the impedance lattice had been proposed. The convergence of the approximate solutions to the exact solution had been proved.

Keywords: the boundary integral equations, the speed of convergence, the polynomials of Chebyshev.

For a some class of linear non-autonomous inhomogeneous systems without using of fundamental matrix of non-autonomous systems the sets of controls solving respectively the synthesis problem and the problem of stabilization are constructed. The controls and under given order its derivatives satisfy the preassigned constraints.

Keywords: linear non-autonomous inhomogeneous control system, synthesis problem, inertial controls..

Multipoint boundary value problem is considered in the multilayer, clarified conditions for the correctness of such a problem, we prove the existence of any well-posed problem for equations of this class, as well as what turns pseudodifferential operators can perturb the task to keep it correctly.

Keywords: theory of pseudo-differential equations, boundary value problem, the Fourier transform method.

The stabilization problem for nonlinear uncontrollable with respect to the first approximation system $\dot x_1=u$, $\dot x_2=x_1$, \ldots, $\dot x_{n-1}=x_{n-2}$, $\dot x_n=x_{n-1}^{2k+1}$ is considered in this work. The construction of stabilizing control is based on Lyapunov function method, attraction domain is described.

Keywords: nonlinear stabilization, nonlinear systems, Lyapunov function method.

Lyapunov matrix equations widely used in the theory of stability of motion, as well as the solution of differential Riccati equations. If the structure of the general solution of the homogeneous part of the Lyapunov equation is well studied, the solution of the inhomogeneous Lyapunov equation is quite cumbersome. We have proposed a formula for constructing a particular solution of the nonhomogeneous Lyapunov equation.

Keywords: Lyapunov matrix equation, Riccati matrix equation, pseudoinverse operator.