краевая задача

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.

Creep and Long-Term Strength Modeling for Thick-Walled Tubes under Combined Loading with Axial Force, Torsional Moment and Internal Pressure

Authors: Radchenko V. P., Tsvetkov V. V.

We have developed a method for solving the boundary-value problem of rheological deformation and creep rupture of thick-walled tube under combined loading with axial force, torsional moment and internal pressure. Energetic variant of the theory of creep and long-term strength is used to describe creep process. Experimental verification of proposed method has been performed using known test data for creep and long-term strength of thick-walled tubes made of D16T alloy and Steel~20. Calculated dependencies for total axial strain and torsion angle on time are obtained.

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.

A Boundary-Value Problem with Shifted for a Mixed Type Equation with Fractional Derivative

Authors: Repin O. A., Sayganova S. A.

A non-local problem for a mixed type equation with partial fractional derivative of Riemann – Liouville is studied, boundary condition of which contains linear combination of generalized operators of fractional integro-differentiation. Unique solvability of the problem is then proved.

Solvability of Boundary Value Problems for the Schrodinger Equation with Purely Imaginary Coefficient

Authors: Mahmudov N. M.

The paper examines regional problems for nonlinear Schrodinger equation when factor of the equation is the square-summable function that has a square-summable derivative. In this process, theorems of existence and uniqueness of the solution of the boundary value problems under consideration have been proved.

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.

Аbout Some Boundary Problems in the Semispace for a Class of Pseudo-Differential Equations with Degeneracy

Authors: Baev A. D.

Boundary problems in the halfspace for one class of the pseudodifferential equations are considered. The coercetive a priori estimations and theorems of the existence of solutions for these problems are established.

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.

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.