# boundary value problem

## On One Exceptional Case of the First Basic Three-Element Carleman-Type Boundary Value Problem for Bianalytic Functions in a Circle

This article considers a non-degenerate (nonreducible to two-element) three-element problem of Carleman type for bianalytic functions in an exceptional case, that is, when one of the coefficients of the boundary condition vanishes at a finite number of contour points. The unit circle is taken as the contour. For this case, an algorithm for solving the problem is constructed, which consists in reducing the boundary conditions of this problem to a system of four Fredholm type equations of the second kind.

## Three-element problem of Carleman type for bianalitic functions in a circle

The article is devoted to the investigation of three-element boundary value problem of Carleman type for bianalytic functions. A constructive method for solution in a circle was found for the case when the problem was not reducible to a two-element boundary value problems without a shift.

## A Case of an Explicit Solutions for the Three-element Problem of Carleman Type for Analytic Functions in a Circle

The article investigates the three-element Carleman boundary value problem in the class of analytic functions, continuous extension to the contour in the Holder sense, when this problem can not be reduced to a two-element boundary value problems . The unit circle is considered as the contour .To be speciﬁc, we study a case of inverse shift. In this case, the solution of the problem is reduced to solving a system of two integral equations of Fredholm second kind; thus signiﬁcantly used the theory of F. D. Gakhov about Riemann boundary value problem for analytic functions.

## A Mixed Problem for a System of First Order Differential Equations with Continuous Potential

We study a mixed problem for a ﬁrst order differential system with two independent variables and continuous potential when the initial condition is an arbitrary square summable vector-valued function. The corresponding spectral problem is the Dirac system. It sets the convergence almost everywhere of a formal decision, obtained by the Fourier method. It is shown that the sum of a formal decision is a generalized solution of a mixed problem, understood as the limit of classical solutions for the case of smooth approximation of the initial data of the problem.

## About Nonsingularity of One Boundary Value Problem of Forth Order with Derivatives by Measure

In the work sufﬁcient conditions for nonsingularity of boundary value problem of forth order with derivatives by measure are obtained.

## Tricomi Problem for Differential-Difference Equations of Mixed

The paper examines the boundary value problem for mixed type equations with two perpendicular lines of degeneracy and the delay in the derivative.

## Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

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

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