A NONSMOOTH 2 POINTS BOUNDARY-VALUE PROBLEM ON RIEMANNIAN-MANIFOLDS

Let (M, [,](R)) be a Riemannian manifold, x(0), x(1) epsilon M and V:M --> R a locally Lipschitz continuous potential function. In this paper we look for the solutions x: [ 0, 1] --> --> M of the differential inclusion 0.1 D-t x(t) epsilon partial derivative V(x(t)) with boundary conditions 0.2 x(0) = x(0), x(1) = x(1) where D(t)x(t) denotes the covariant derivative of x(t) along the direction of x(t) and partial derivative V(x(t)) the generalized gradient of V in x(t). Using a variant of the Lusternik-Schnirelman critical point theory, we state the existence of infinitely many solutions of problem (0.1)-(0.2) when M is not contractible in itself.