We investigate nodal radial solutions to semilinear problems of type −Δu=f(|x|,u)inΩ,u=0on∂Ω,where Ω is a bounded radially symmetric domain of RN (N≥2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's / Amadori, A. L.; Gladiali, F.. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - 55:(2020), pp. 103-133. [10.1016/j.nonrwa.2020.103133]
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's
Gladiali F.
2020-01-01
Abstract
We investigate nodal radial solutions to semilinear problems of type −Δu=f(|x|,u)inΩ,u=0on∂Ω,where Ω is a bounded radially symmetric domain of RN (N≥2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.| File | Dimensione | Formato | |
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