Radial and non-radial solutions for the Lane-Emden problem in the disk

Abstract: We discuss sharp asymptotic analysis results on radial solutions of the Lane-Emden problem in the disk, which in particular lead to a Morse index formula. As a consequence we can prove the existence of new unexpected solutions. The talk is based on results mainly contained in [ADI], [IS], [GI] and [DIP].

[ADI] A. Amadori, F. De Marchis, I. Ianni, Morse index computation for radial solutions of the Henon problem in the disk, preprint

[IS] I. Ianni, A. Saldana, Sharp asymptotic behavior of radial solutions of some planar semilinear elliptic problems, preprint

[GI] I. Ianni, F. Gladiali, Quasi-radial solutions for the Lane-Emden problem in the ball, NoDEA 27 (2) (2020)

[DIP] F. De Marchis, I. Ianni, F. Pacella, Exact Morse index computation for nodal radial solutions of Lane-Emden problems, Mathematische Annalen 367 (2017)

analysis of PDEs

Audience: researchers in the topic

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Rio de Janeiro webinar on analysis and partial differential equations

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