Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two
Kefan PAN , Shuying TIAN , Pingping YANG
Journal of Partial Differential Equations ›› 2025, Vol. 38 ›› Issue (3) : 335 -351.
Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two
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 mm eigenvalues and eigenfunctions of the linearized Lane-Emden problem in dimension two, and correspondingly the number of concentrated points of the first mm eigenfunctions are given.
Lane-Emden problem / eigenfunctions and eigenvalues / asymptotic behavior
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