Eringen’s non-local elasticity theory in its integral formulation: some exact dynamic solutions

Eringen’s original theory of non-local elasticity defines non-local stresses as an integral (a functional) of the local stresses. Later, he transformed his theory into another that dispenses with the integral in favour of partial differential equations (PDEs). However, it is known that this theory (although simpler) is not equivalent to the original. Here, equations from the original theory are solved exactly, for antiplane waves in an elastic halfspace.