  We examine the BRS invariance of the open pure spinor superstring in the
presence of background superfields on a Dp-brane. It is shown that the BRS
invariance leads not only to boundary conditions on the spacetime spinors, but
also to supersymmetric DBI equations of motion for the background superfields
on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI
equations for a D9-brane.
