The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

Solutions are obtained for the boundary value problem, y(n) + f(x, y) = 0, y(i)(0) = y(1) = 0, 0 ≤ i ≤ n − 2, where f(x, y) is singular at y = 0. An application is made of a fixed point theorem for operators that are decreasing with respect to a cone. §

It is shown that the non-homogeneous Dirichlet and Neuman problems for the 2-order Seiberg-Witten equation admit a regular solution once the H-condition 3.1.1 is satisfied. The approach consist in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation.

we consider a mixed boundary value problem for a quarter-plane with a robin condition on one edge. we have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

This paper reviews developments in the theory of boundary critique, which has been used in a number of OR projects to support conflict resolution. The authors argue that this theory (and associated models) is also useful for conflict prevention. It indicates the need to support people in discussing their differences before conflict arises. Potential conflicts can be reframed through dialogue fo...