  In this paper, we extend Rabinowitz Floer homology theory which has been
established and extensively studied for hypersurfaces to coisotropic
submanifolds of higher codimension. With this generalized version of Rabinowitz
Floer homology theory, we explore the coisotropic intersection problem which
interpolates between the Lagrangian intersection problem and the closed orbit
problem. To be specific, we study the existence of leafwise intersection points
on contact coisotropic submanifolds and the displaceability of stable
coisotropic submanifolds.
