on the existence, uniqueness, and basis properties of radial eigenfunctions of a semilinear second-order elliptic equation in a ball
Clicks: 147
ID: 229098
2009
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This
article has not been analysed, so there is no overall score โ
reader engagement is measured and shown alongside.
Reader Engagement
Emerging Content
30.0
/100
147 views
10 readers
AI Quality Assessment
Not analyzed
Readership in this journal
EmergingRanked #49 of 403 articles by views in structural engineering and mechanics
Most read
Least read
Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 403 in total.
Mint this article as an NFT
Not yet mintedCreate a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.
5
SUSD
one-off · no wallet required
Abstract
We consider the following eigenvalue problem: โฮ๐ข+๐(๐ข)=๐๐ข, ๐ข=๐ข(๐ฅ), ๐ฅโ๐ต={๐ฅโโ3โถ|๐ฅ|<1}, ๐ข(0)=๐>0, ๐ข||๐ฅ|=1=0, where ๐ is an arbitrary fixed parameter and ๐ is an odd smooth function. First, we prove that for each integer ๐โฅ0 there exists a radially symmetric eigenfunction ๐ข๐ which possesses precisely ๐ zeros being regarded as a function of ๐=|๐ฅ|โ[0,1). For ๐>0 sufficiently small, such an eigenfunction is unique for each ๐. Then, we prove that if ๐>0 is sufficiently small, then an arbitrary sequence of radial eigenfunctions {๐ข๐}๐=0,1,2,โฆ, where for each ๐ the ๐th eigenfunction ๐ข๐ possesses precisely ๐ zeros in [0,1), is a basis in ๐ฟ๐2(๐ต) (๐ฟ๐2(๐ต) is the subspace of ๐ฟ2(๐ต) that
consists of radial functions from ๐ฟ2(๐ต). In addition, in the latter case, the sequence {๐ข๐/โ๐ข๐โ๐ฟ2(๐ต)}๐=0,1,2,โฆ is a Bari basis in the same space.
| Reference Key |
zhidkov2009internationalon
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Peter Zhidkov |
| Journal | structural engineering and mechanics |
| Year | 2009 |
| DOI |
10.1155/2009/243048
|
| URL | |
| Keywords |
Citations
No citations found. To add a citation, contact the admin at info@scimatic.org
Comments
No comments yet. Be the first to comment on this article.