Solutions to nonlocal Neumann boundary value problems

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...

Nonlocal Problems with Neumann Boundary Conditions

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...

Positive Solutions of Some Higher Order Nonlocal Boundary Value Problems

We show how a unified method, due to Webb and Infante, of tackling many nonlocal boundary value problems, can be applied to nonlocal versions of some recently studied higher order boundary value problems. In particular, we give some explicit examples and calculate the constants that are required by the theory.

Positive Solutions of Some Nonlocal Boundary Value Problems

Uniqueness of Solutions for Fourth-order Nonlocal Boundary Value Problems

Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation, y (4) = f (x, y, y , y , y), satisfying 5-point, 4-point, and 3-point nonlocal boundary conditions. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any medium, pr...