Precise Spectral Asymptotics for Nonlinear Sturm–Liouville Problems

• Shibata, Tetsutaro

抄録

We consider the nonlinear Sturm–Liouville problem-u″(t)+u(t)p=λu(t), u(t)>0, tI(0, 1), u(0)=u(1)=0, where p>1 is a constant and λ>0 is an eigenvalue parameter. To understand the global structure of the bifurcation diagram in R+×L2(I) completely, we establish the asymptotic expansion of λ(α) (associated with eigenfunction uα with uα2=α) as α→∞. We also obtain the corresponding asymptotics of the width of the boundary layer of uα as α→∞.

収録刊行物

• Journal of Differential Equations

  Journal of Differential Equations 180 (2), 374-394, 2002-04-10

  Elsevier Science

詳細情報

• CRID: 1050859215940440832
• NII論文ID: 120000875861
• NII書誌ID: AA00696680
• Web Site: http://ir.lib.hiroshima-u.ac.jp/00021528
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
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  • CiNii Articles
  • KAKEN