boundary value problem

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

Authors: Perelman N. R.

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.

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.

Tricomi Problem for Differential-Difference Equations of Mixed

Authors: Lashtabega О. V., Zarubin А. N.

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

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

Authors: Golovaneva F. V.

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

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

Authors: Perelman N. R.

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

Authors: Burlutskaya M. S.

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.

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

Authors: Perelman N. R., Rasulov K. M.

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.