@Article{JPDE-38-335,
author = {Pan , KefanTian , Shuying and Yang , Pingping},
title = {Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two},
journal = {Journal of Partial Differential Equations},
year = {2025},
volume = {38},
number = {3},
pages = {335--351},
abstract = {<p style="text-align: justify;">Recently, qualitative analysis of peaked solutions of Lane-Emden problem
 in dimension two has been widely considered. In particular, the Morse index of concentrated solutions with a single peak or multi peaks has been computed in [15,16]
 separately. In this paper, we continue to consider the qualitative properties of the
 eigenvalues and eigenfunctions of the linearized Lane-Emden problem associated to
 peak solutions. Here we establish the fine behaviors of the first $m$ eigenvalues and
 eigenfunctions of the linearized Lane-Emden problem in dimension two, and correspondingly the number of concentrated points of the first $m$ eigenfunctions are given.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v38.n3.6},
url = {http://global-sci.org/intro/article_detail/jpde/24416.html}
}