TY - JOUR AU - Castro, Alfonso AU - Ventura, Ivan PY - 2016/11/23 Y2 - 2024/03/28 TI - Existence of solutions to a semilinear elliptic boundary value problem with augmented Morse index bigger than two JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 49 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2016.075 SP - 233 - 244 AB - Building on the construction of least energy sign-changing solutions to variational semilinear elliptic boundary value problems introduced in \cite{ccn}, we prove the existence of a solution with {\it 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. ER -