Armenak Babayan

National Polytechnic University of Armenia · Department of Applied Mathematics and Physics

We consider the Dirichlet problem for the linear non-elliptic fourth order partial differential equation in the unit disk. It supposed that in the equation only fourth order terms and coefficients are constant. The solvability conditions of in-homogeneous problem and the solutions of the corresponding homogeneous problem are determined in explicit...

The Dirichlet problem for sixth order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of homogeneous problem and the number of linearly indep...

The Dirichlet problem for sixth-order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of the homogeneous problem and the number of linearly i...

Рассматривается задача Дирихле для одного класса правильно эллиптических уравнений шестого порядка в единичном круге. Получены формулы для определения дефектных чисел этой задачи. Линейно независимые решения однородной задачи и условия разрешимости неоднородной задачи определяются в явном виде. Библиография: 15 названий.

The Dirichlet problem for a class of properly elliptic sixth-order equations in the unit disk is considered. Formulas for determining the defect numbers of this problem are obtained. Linearly independent solutions of the homogeneous problem and conditions for the solvability of the inhomogeneous problem are given explicitly.

In this paper we present the numerical method for the solution of the Riemann problem for the second-order improperly elliptic equation. First, we reduce this problem to boundary value problems for properly elliptic equations, and after that we solve these problems by the grid method. MSC: 35G45, 35G15, 35J25, 35J57, 65N06, 65N20.

A boundary value problem for the Bitsadze equation $$\frac{{\partial ^2 }}{{\partial \bar z^2 }}u(x,y) \equiv \frac{1}{4}\left( {\frac{\partial }{{\partial x}} + i\frac{\partial }{{\partial y}}} \right)^2 u(x,y) = 0$$ in the interior of the unit disc is considered. It is proved that the problem is Noetherian and its index is calculated, and solv...

We consider a boundary value problem in the unit disk for an elliptic equation of order N with constant coefficients. We suppose, that the characteristic equation has exactly M pairs of complex conjugate roots (0≤2M≤N). The solution of this problem belongs to the class of N times continuously differentiable functions, which with up to the (N-M-1)-t...

The paper studies the unique solvability of the Dirichlet problem for some class of higher order properly elliptic equations. The different forms of necessary and sufficient conditions rendering the corresponding problem in being uniquely solvable and some applications are found.

The paper studies the unique solvability of a Dirichlet problem for some class of properly elliptic fourth-order equations. Necessary and sufficient conditions as well as some sufficient conditions rendering the corresponding problem uniquely solvable are found.

The paper studies unique solvability in the open unit disk of the Dirichlet problem for a properly elliptic equation of order 2n in the class of 2n times continuously differentiate functions, which with up to n-th order derivatives satisfy the Hölder condition in the closed disk. The necessary and sufficient conditions for unique solvability are fo...

The paper studies boundary value problems for some systems of nonlinear ordinary differential equations, that have important applications. The existence of a solution in a finite interval with starting point fixed, whose endpoint has to be determined from the boundary conditions is proved, and estimates that allow a construction of approximate solu...

The paper considers a Dirichlet-type boundary value problem for the elliptic equation ∂ m+n u ∂z ¯ m ∂z n =0,∂u ∂z ¯≡1 2∂u ∂x+i∂u ∂y,∂u ∂z≡1 2∂u ∂x-i∂u ∂y in a multiply connected domain. The problem is reduced to a Dirichlet problem for the n-harmonic equation. An existence theorem is proved.