A non-smooth two points boundary value problem on Riemannian manifolds
The problem considered is to find solutions to the differential inclusion problem: \[ D_t x(t)\in \partial V(x(t))\;(\text{generalized gradient}) \] with boundary conditions \(x(0)= x_0\), \(x(1)= x_1\), on a Riemannian manifold. Here \(V\) is a locally Lipschitz continuous potential function. By an argument using the Lyusternik-Shnirelman critical point theory it is proven that, unless the manifold is contractible in itself, there are infinitely many solutions to this problem.
Lyusternik- Shnirelman critical point theory
scientific article; zbMATH DE number 711481