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Volume 38, Issue 3
Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two

Kefan Pan, Shuying Tian & Pingping Yang

DOI: 10.4208/jpde.v38.n3.6

J. Part. Diff. Eq., 38 (2025), pp. 335-351.

Published online: 2025-09

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  • Abstract

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.

  • Keywords

Lane-Emden problem, eigenfunctions and eigenvalues, asymptotic behavior.

  • AMS Subject Headings

35A02, 35J08, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@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 = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v38.n3.6}, url = {http://global-sci.org/intro/article_detail/jpde/24416.html} }
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 -

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.

Pan , KefanTian , Shuying and Yang , Pingping. (2025). Fine Behaviors of Eigenvalues and Eigenfunctions of the Lane-Emden Problem in Dimension Two. Journal of Partial Differential Equations. 38 (3). 335-351. doi:10.4208/jpde.v38.n3.6
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