Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

Year:    2022

Author:    Ruggero Freddi

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 26–78

Abstract

In this paper we consider the Dirichlet problem

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where $\rho$ is a small parameter and $\Omega$ is a $C^2$ bounded domain in $\mathbb{R}^2$. In [1], the author proves the existence of a $m$-point blow-up solution $u_\rho$ jointly with its asymptotic behaviour. We compute the Morse index of $u_\rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2020-0037

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 26–78

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    53

Keywords:    Morse index sinh-Poisson equation eigenvalues estimates.

Author Details

Ruggero Freddi