A RELLICH TYPE IDENTITY AND APPLICATIONS

arbitrary given u∈C2(Ω _ ), where Ω is a smooth bounded domain contained in RN. This intrinsic identity has played an important role in many contexts in the theory of partial differential equations. Some earlier applications were considered by Rellich himself, Payne and Weinberger [8] and Nehari [7]. In [9] Pohozaev rediscovered a modified version of RellichOs identity in the study of eigenvalue problems of the form