We investigate nodal radial solutions to semilinear problems of type [egincases-Delta u = f(|x|,u) qquad & ext in Omega, ewline u= 0 & ext on partial Omega, endcases ] where $Omega$ is a bounded radially symmetric domain of $mathbb R^N$ ($Nge 2$) 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

Anna Lisa Amadori;
2020

Abstract

We investigate nodal radial solutions to semilinear problems of type [egincases-Delta u = f(|x|,u) qquad & ext in Omega, ewline u= 0 & ext on partial Omega, endcases ] where $Omega$ is a bounded radially symmetric domain of $mathbb R^N$ ($Nge 2$) 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/76401
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