# 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},
journal={Nonlinearity},
year={2018},
volume={33},
pages={2541 - 2561}
}
• Published 11 May 2018
• Mathematics
• Nonlinearity
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…
• Mathematics
• 2020
We consider the semilinear elliptic problem where B is the unit ball of $${\mathbb {R}}^2$$ R 2 centered at the origin and $$p\in (1,+\infty )$$ p ∈ ( 1 , + ∞ ) . We prove the existence of
In this paper we consider the Henon problem in the ball with Dirichlet boundary conditions. We study the asymptotic profile of radial solutions and then deduce the exact computation of their Morse
• Mathematics
• 2022
. We construct a smooth radial positive solution for the following m -coupled elliptic system (cid:2) for β > 0 large enough, where f ∈ C 2 , 1 ( R ) , f (0) = 0, B 1 (0) ⊂ R N is the unit ball
• Mathematics, Computer Science
Nonlinear Analysis: Real World Applications
• 2019
We prove the existence of nonradial solutions for the Hénon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent α. For sign-changing solutions the case α =
We prove the existence of nonradial solutions for the Henon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent \begin{document}$\alpha$\end{document} .