TY - JOUR
T1 - Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two
AU - Pan , Kefan
AU - Tian , Shuying
AU - Yang , Pingping
JO - Journal of Partial Differential Equations
VL - 3
SP - 335
EP - 351
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/jpde.v38.n3.6
UR - https://global-sci.org/intro/article_detail/jpde/24416.html
KW - Lane-Emden problem, eigenfunctions and eigenvalues, asymptotic behavior.
AB - <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>