Abstract
Building on the construction of least energy sign-changing solutions to variational semilinear elliptic boundary value problems introduced in [A. Castro, J. Cossio and J.M. Neuberger, Sign changing solutions for a superlinear Dirichlet problem, Rocky Mountain J. Math. 27 (1997), 1041--1053], 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.
Citation
Alfonso Castro. Ivan Ventura. "Existence of solutions to a semilinear elliptic boundary value problem with augmented Morse index bigger than two." Topol. Methods Nonlinear Anal. 49 (1) 233 - 244, 2017. https://doi.org/10.12775/TMNA.2016.075
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