Existence of solutions to a semilinear elliptic boundary value problem with augmented Morse index bigger than two - Castro, Alfonso; Ventura, Ivan (Topological Methods in Nonlinear Analysis, 2016)
Building on the construction of least energy sign-changing solutions to variational semilinear elliptic boundary value problems introduced in ccn, we prove the existence of a solution with augmented Morse index at least three when a sublevel of the corresponding action functional has nontrivial topology. We provide examples where the set of least energy sign changing solutions is disconnected, hence has nontrivial topology.