Browse

You are looking at 1 - 10 of 43 items for :

  • Applied Mathematics x
Clear All
Open access

Hatem Najar and Monia Raissi

Abstract

We give the eigenvalues asymptotics for the Stark operator of the form −Δ+F x, F > 0 on L2([0, d]). This is given in the case when F is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics of the specialized Airy functions.

Open access

Charyyar Ashyralyyev

Abstract

Reverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

Open access

Makhmud A. Sadybekov

Abstract

In this paper, a new finite difference method to solve nonlocal boundary value problems for the heat equation is proposed. The most important feature of these problems is the non-self-adjointness. Because of the non-self-adjointness, major difficulties occur when applying analytical and numerical solution techniques. Moreover, problems with boundary conditions that do not possess strong regularity are less studied. The scope of the present paper is to justify possibility of building a stable difference scheme with weights for mentioned type of problems above.

Open access

Dovlet M. Dovletov

Abstract

Sturm-Liouville operator with second kind of nonlocal boundary value conditions is considered. For the classical solution, a priori estimate is established and unique existence is proved. Associated finite-difference scheme is proposed on uniform mesh and second-order accuracy for approximation is proved. An application of obtained results to nonlocal boundary problems with weight integral conditions is provided.

Open access

Assia Guezane-Lakoud and Kheireddine Belakroum

Abstract

This paper deals with the existence of solutions for a class of boundary value problem (BVP) of fractional differential equation with three point conditions via Leray-Schauder nonlinear alternative. Moreover, the existence of nonnegative solutions is discussed.

Open access

Mısır J. Mardanov, Yagub A. Sharifov and Kamala E. Ismayilova

Abstract

This paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

Open access

Tuhtasin G. Ergashev

Abstract

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables.

Open access

Alexander Kiselev, Mikhail Chernobay, Omar Lazar and Chao Li