Existence of solutions to a semilinear elliptic boundary value problem with augmented Morse index bigger than two
Keywords
Subcritical semilinear elliptic equation, critical point, Morse index, homotopy groups, Nehari manifold, mountain pass lemma, deformation lemmaAbstract
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.References
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