Blow-up solutions concentrated along minimal submanifolds for some supercritical elliptic problems on Riemannian manifolds

Let (M, g) and be two Riemannian manifolds of dimensions m and k, respectively. Let . The warped product is the (m + k)-dimensional product manifold furnished with metric . We prove that the supercritical problem has a solution concentrated along a k-dimensional minimal submanifold of as the real parameter goes to zero, provided the function h and the sectional curvatures along satisfy a suitable condition.