Weakly nonlocal boundary value problems with application to geology

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...

A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems

Abstract. We develop a calculus for nonlocal operators that mimics Gauss’ theorem and the Green’s identities of the classical vector calculus. The operators we define do not involve the derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal “boundaryvalue” problems that mimic the Dirichlet and Neumann problems for second-order scalar elliptic partial dif...

Nonlocal Elliptic Boundary Value Problems

Solvability of Nonlocal Fractional Boundary Value Problems

An Existence Principle for Nonlocal Difference Boundary Value Problems with -Laplacian and Its Application to Singular Problems

Let R 0,∞ and let Z denote the set of all integers. If a, b ∈ Z, a < b, then T a, b denotes the discrete interval {a, a 1, . . . , b}. LetΔu k u k 1 −u k be the forward difference operator. Let T,N ∈ Z, T < N, and let X stand for the space of functions u : T T − 1,N 1 → R equipped with the norm ‖u‖ max{|u k | : k ∈ T T − 1,N 1 }. Clearly, X is an N − T 3 dimensional Banach space. Denote byA the...