Existence of solutions to a semilinear elliptic boundary value problem with augmented Morse index bigger than two. (English) Zbl 1370.35018

Summary: Building on the construction of least energy sign-changing solutions to variational semilinear elliptic boundary value problems introduced in [the first author et al., Rocky Mt. J. Math. 27, No. 4, 1041–1053 (1997; Zbl 0907.35050)], 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.


35A16 Topological and monotonicity methods applied to PDEs
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J61 Semilinear elliptic equations


Zbl 0907.35050
Full Text: DOI Euclid