Solutions of some nonlinear elliptic problems, which are singular on a submanifold

AbstractLet (M, g) be a C2 complete connected Riemannian manifold of dimension N ≥ 3 and Σ a compact submanifold of M of dimension d ≥ 0 without boundary. First under some assumptions on h, we prove that Σ is a removable singularity for the equation −Δgu + h(x,u) = 0 in M⧹Σ. Secondly if M is compact and h(x,u) = |u|q−1 u, q > 1 or h(x,u) = eu, we construct solutions of that equation which blow-up on Σ, under some conditions on N, d and q