Introduction

Abstract

Differential equations containing values of unknown functions and their derivatives at different points of a manifold are called nonlocal differential equations. The simplest equation of this type has the form

$$ D_1 u\left( x \right) + D_2 u\left( {g\left( x \right)} \right) = f\left( x \right),x \in \Omega , $$

where D₁ and D₂ are some differential operators, u is the unknown function, and g: Ω → Ω is a self-mapping of the domain where the equation is considered. We shall consider only equations in which the mapping g is invertible.