Article - postprint
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.
© 2017 Juliusz P. Schauder Centre for Nonlinear Studies
This work is licensed under a Creative Commons Attribution 4.0 License.
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.