# On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II

@article{Amadori2018OnAS, title={On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s: II}, author={Anna Lisa Amadori and Francesca Gladiali}, journal={Nonlinearity}, year={2018}, volume={33}, pages={2541 - 2561} }

By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in Amadori A L and Gladiali F (2018 arXiv:1805.04321), we give a lower bound for the Morse index of radial solutions to Hénon type problems −Δu=|x|αf(u)inΩ,u=0on∂Ω, where Ω is a bounded radially symmetric domain of RN (N ⩾ 2), α > 0 and f is a real function. From this estimate we get that the Morse index of nodal radial solutions to this problem goes to ∞ as…

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\begin{equation*} (H) \qquad \qquad \left \{
\begin{aligned}
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