Abel–Gontscharoff boundary value problems on measure chains

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

On Equivariant Boundary Value Problems

smooth coefficients aα(x), L+ be a formally adjoint differential operation. Let L0, L0 be minimal operators (i.e., for example, D(L0) is the clozure of C∞ 0 (Ω) in the norm of the graph ‖u‖L = ‖u‖L2(Ω)+‖Lu‖L2(Ω)), and L, L+ be maximal expansions of L,L+ in the space L2(Ω) respectively (i.e. L = (L0 ) ∗, L+ = (L0)∗), L̃ = L|D(L̃) where D(L̃) is the clozure of C∞(Ω̄) in the norm of the graph ‖u‖L and...

On Matrix Boundary Value Problems

Introduction. In a recent publication1 a matrix type of boundary value problem was introduced in order to simplify the description of nuclear reactions. It appeared that this type of boundary value problem could find applications in other branches of mathematical physics, and the purpose of the present note is to illustrate them. When we deal with vibrations of continuous media, with problems o...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Nonlocal Boundary Value Problems

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...