Precise Spectral Asymptotics for Nonlinear Sturm–Liouville Problems
Journal of Differential Equations Volume 180 Issue 2
Page 374-394
published_at 2002-04-10
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| File | |
| Title ( eng ) |
Precise Spectral Asymptotics for Nonlinear Sturm–Liouville Problems
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| Creator | |
| Source Title |
Journal of Differential Equations
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| Volume | 180 |
| Issue | 2 |
| Start Page | 374 |
| End Page | 394 |
| Abstract |
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→∞.
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Elsevier Science
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| Date of Issued | 2002-04-10 |
| Rights |
Copyright (c) 2002 Elsevier Science (USA).
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0022-0396
[DOI] 10.1006/jdeq.2001.4061
[NCID] AA00696680
[DOI] http://dx.doi.org/10.1006/jdeq.2001.4061
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