SOLUTIONS OF SOME NONLINEAR ELLIPTIC PROBLEMS, WHICH ARE SINGULAR ON A SUBMANIFOLD

Let (M,g) be a C-2 complete connected Riemannian manifold of dimension N greater than or equal to 3 and C a compact submanifold of M of dime nsion d greater than or equal to 0 without boundary. First under some assumptions on h, we prove that Sigma is a removable singularity for t he equation -Delta u + h(x,u) = 0 in M\Sigma. Secondly if M is compact and h(x,u) = \u\(q-1)u, q > 1 or h(x,u) = e(u), we construct solution s of that equation which blow-up on Sigma, under some conditions on N, d and q.