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Volume 38, Issue 1
Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

Ruggero Freddi

Anal. Theory Appl., 38 (2022), pp. 26-78.

Published online: 2021-12

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  • Abstract

In this paper we consider the Dirichlet problem

2.JPG

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.

  • AMS Subject Headings

35P30, 35B40

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COPYRIGHT: © Global Science Press

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@Article{ATA-38-26, author = {Ruggero Freddi , }, title = {Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {38}, number = {1}, pages = {26--78}, abstract = {

In this paper we consider the Dirichlet problem

2.JPG

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0037}, url = {http://global-sci.org/intro/article_detail/ata/20011.html} }
TY - JOUR T1 - Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation AU - Ruggero Freddi , JO - Analysis in Theory and Applications VL - 1 SP - 26 EP - 78 PY - 2021 DA - 2021/12 SN - 38 DO - http://doi.org/10.4208/ata.OA-2020-0037 UR - https://global-sci.org/intro/article_detail/ata/20011.html KW - Morse index, sinh-Poisson equation, eigenvalues estimates. AB -

In this paper we consider the Dirichlet problem

2.JPG

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.

Ruggero Freddi , . (2021). Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation. Analysis in Theory and Applications. 38 (1). 26-78. doi:10.4208/ata.OA-2020-0037
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