New Trends on Nonlocal and Functional 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 Elliptic Boundary Value Problems

Solvability of Nonlocal Fractional Boundary Value Problems

Quasilinearization Method and Nonlocal Singular Three Point Boundary Value Problems

The method of upper and lower solutions and quasilinearization for nonlinear singular equations of the type −x(t) + λx(t) = f(t, x(t)), t ∈ (0, 1), subject to nonlocal three-point boundary conditions x(0) = δx(η), x(1) = 0, 0 < η < 1, are developed. Existence of a C1 positive solution is established. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solut...

Positive Solutions and Eigenvalues of Nonlocal Boundary-value Problems

We study the ordinary differential equation x′′ + λa(t)f(x) = 0 with the boundary conditions x(0) = 0 and x′(1) = R 1 η x ′(s)dg(s). We characterize values of λ for which boundary-value problem has a positive solution. Also we find appropriate intervals for λ so that there are two positive solutions.