  The aim of this paper is to study differential properties of orthogonal
polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass
point at $-1$ and/or $+1$. In particular, we construct the orthogonal
polynomials using certain Casorati determinants. Using this construction, we
prove that when the Jacobi parameters $\alpha$ and $\beta$ are nonnegative
integers the Jacobi-Sobolev orthogonal polynomials are eigenfunctions of a
differential operator of finite order (which will be explicitly constructed).
Moreover, the order of this differential operator is explicitly computed in
terms of the matrices which define the discrete Jacobi-Sobolev bilinear form.
