Mathematics

On Multiple Completeness of the Root Functions of the Pencils of Differential Operators with Constant Coefficients

Authors: Rykhlov V. S., Parfilova O. V.

A class of the pencils of ordinary differential operators of n-th order with constant coefficients is considered. The roots of the characteristic equation of the pencils from this class are supposed to lie on a straight line containing the origin, provided that one of the roots lies on one part from the origin, the rest lie on another part. The cases when the system of root functions is m-fold (3 ≤ m ≤ n − 1) complete in the space of square summable functions on main interval are described.

Estimation of Operator Norms in Eigenvalue Problems for Equations with Discontinuous Operators

Authors: Potapov D. K.

Existence of solutions of problems with a spectral parameter for the equations with discontinuous operators is considered. The estimations of the operator norms for these problems are received. Dirichlet problem for the higher-order elliptic equation with discontinuous nonlinearity is considered as an appendix.

Finding of Accessory Parameters for Mixed Inverse Boundary Value Problem with Polygonal Known Part of Boundary

Authors: Nasyrov S. R., Nizamieva L. Y.

We consider a mixed inverse boundary value problem with respect to parameter x for the case when the known part of the boundary L1z is a polygonal line. Integral representation of solution to the problem depends on real parameters being the pre-images of the vertices of L1z under conformal mapping. By analogy with Schwartz – Christoffel integrals, we name them accessory parameters. It is suggested a new method of determining the accessory parameters.

On Idempotent Elements of Semigroup of Increasing Monotonous Mappings

Authors: Kryukova A. L.

In some special classes of ordered topological spaces we characterize roundings as extreme points of set of non increasing isotonic mappings, and establish their stability in Hyers –Ulam sense.

Solvability of Evolutionary Equations in Generalized Transmission Problems for Shallow Shells

Authors: Kirichenko V. F.

We prove the solvability of the generalized transmission problem in the non-classical theory of shallow shells using the method of compactness and a new way of obtaining a priori estimates.

On Classical Solvability of One-Dimensional Mixed Problem for Fourth Order Semilinear Biparabolic Equations

Authors: Khudaverdiyev K. I., Heydarova M. N.

Existence and uniqueness of classical solution of one-dimensional mixed problem with Riquier type homogenous boundary conditions for one class of fourth order semilinear biparabolic equations are studied. A priori estimates method is used to prove the existence in large theorem for classical solution of mixed problem under consideration..

On the Number of Solutions of Nonlinearity Boundary Value Problems with a Stieltjes Integral

Authors: Davidova M. B., Shabrov S. A.

In this paper we obtain sufficient conditions for the existence of multiple solutions for nonlinear boundary value problem with a Stieltjes integral.

Substantiation of Fourier Method in Mixed Problem with Involution

Authors: Burlutskaya M. S., Khromov A. P.

In this paper the mixed problem for the first order differential equation with involution is investigated. Using the received specified asymptotic formulas for eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to transform a series representing the formal solution on Fourier method, and to prove the possibility of its term by term differentiation. At the same time on the initial problem data minimum requirements are imposed.