One-Sided Nonlocal Boundary-Value Problem for Singular Parabolic Equations

In spaces of classical functions with power weight, we prove the existence and uniqueness of a solution of a one-sided nonlocal boundary-value problem for parabolic equations with an arbitrary power order of degeneracy of coefficients. We obtain an estimate for the solution of this problem in the corresponding spaces.     

非局部非对称弹性理论混合边值问题的提法

从完全的虚功和虚功率原理以及广义Ｐｉｏｌａ定理出发一并推导出非局部非对称弹性理论的运动方程、所有边界条件和全能量方程。把这时给出的边界条件和高键,戴天民的相应结果加在一超即可表述非局部非对称线性弹性理论的混合边值问题。     

A Nonlocal Boundary-Value Problem for Differential Equations with Fractional Time Derivative with Variable Coefficients

Conditions for the existence and uniqueness of a classical solution of a nonlocal boundary-value problem for a differential equation with a regularized Riemann–Liouville fractional time derivative with variable coefficients are investigated.     

Stability of Nonlocal Finite-Difference Problems

The article presents a brief review of the stability theory of finite-difference schemes for time-dependent problems of mathematical physics in which the spatial differential operator is constrained by boundary conditions joined on different pieces of the boundary. It is shown for the particular case of the heat-conduction equation that nonlocal boundary conditions may generate both simple finite-difference operators and finite-difference operators with an incomplete eigenfunction system. In both cases a rule is suggested for constructing the energy norm that ensures stability of the finite-difference scheme.__________Translated from Prikladnaya Matematika i Informatika, No. 17, pp. 72–83, 2004.     

Nonlocal Boundary-Value Problem for a Second-Order Partial Differential Equation in an Unbounded Strip

Ukrainian Mathematical Journal - The conditions of well-posedness of nonlocal boundary-value problems are established for a second-order linear partial differential equation in an unbounded strip...     

Finite-Difference Method for a System of Third-Order Boundary-Value Problems

In this paper, we develop a two-stage numerical method for computing the approximate solutions of third-order boundary-value problems associated with odd-order obstacle problems. We show that the present method is of order two. A numerical example is presented to illustrate the applicability of the new method. A comparison is also given with previously known results.     

Nonlocal Boundary-Value Problem for a Linear Ordinary Differential Equation with Fractional Discretely Distributed Differentiation Operator

Mathematical Notes - A nonlocal boundary-value problem for a linear ordinary differential equation with fractional discretely distributed differentiation operator is considered. The existence and...     

Nonlocal Boundary-Value Problems for Elliptic Systems in Angles

In this paper we consider elliptic systems in plane angle with nonlocal boundary conditions. We prove the existence and uniqueness of the solution in weighted space. For a proof, we study a system of ordinary differential equations with a parameter and nonlocal boundary conditions.     

On The Existence of a Countable Set of Positive Solutions for a Nonlocal Boundary-Value Problem with Vector-Valued Response

ABSTRACT

The existence of a countable set of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated by some variational methods based on the idea of the Fenchel conjugate. As a consequence of a duality developed here, we obtain the existence of a countable set of solutions for our problem that are minimizers to a certain integral functional. We derive (also in the superlinear case) a measure of a duality gap between primal and dual functional for approximate solutions.     

Well-Posed and Regular Nonlocal Boundary-Value Problems for Partial Differential Equations

The present paper deals with the well-posedness and regularity of one class of one-dimensional time-dependent boundary-value problems with global boundary conditions on the entire time interval. We establish conditions for the well-posedness of boundary-value problems for partial differential equations in the class of bounded differentiable functions. A criterion for the regularity of the problem under consideration is also obtained.     

Solvability of Linear Matrix Boundary-Value Problem

We find solvability conditions and give a construction of generalized Green operator for a linear matrix boundary-value problem. We suggest an operator which reduces a linear matrix equation to a standard linearNoetherian boundary-value problem. To solve a linearmatrix systemwe use an operatorwhich reduces a linear matrix equation to a linear algebraic equation with rectangular matrix.     

On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations

Mathematical Notes - We study the solvability of nonlocal boundary-value problems for singular parabolic equations of higher order in which the coefficient of the time derivative belongs to a space...     

Boundary-Value Problem for Functional-Differential Advanced-Retarded Tricomi Equation

We investigate the boundary-value problem for Tricomi mixed-type equation with multiple functional retarding and advancing. We construct the general solution to the equation. The problem is uniquely solvable.