In this paper, the bond-based peridynamic system is analyzed as a nonlocal boundary value problem with volume constraint. The study extends earlier works in the literature on nonlocal diffusion and nonlocal peridynamic models to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on s...

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.