The Basis Property of the System of Weak Eigenfunctions of a Discontinuous Sturm–Liouville Problem
Yazarlar (2)
Doç. Dr. Hayati OLĞAR
Tokat Gaziosmanpaşa Üniversitesi, Türkiye
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale |
| Dergi Adı | Mediterranean Journal of Mathematics |
| Dergi ISSN | 1660-5446 Wos Dergi Scopus Dergi |
| Dergi Tarandığı Indeksler | SCI-Expanded |
| Dergi Grubu | Q4 |
| Makale Dili | İngilizce |
| Basım Tarihi | 06-2017 |
| Cilt No | 14 |
| Sayı | 3 |
| DOI Numarası | 10.1007/s00009-017-0915-9 |
| Makale Linki | http://link.springer.com/10.1007/s00009-017-0915-9 |
| Özet |
| The purpose of this study is to investigate some important spectral properties of one discontinuous Sturm–Liouville problem. By applying our own approaches the considered problem is transformed into an eigenvalue problem for suitable integral equation in terms of which it is defined as a concept of weak eigenfunctions. Then we introduce for consideration some compact operators in such a way that this integral equation can be reduced to the appropriate operator-pencil equation and prove that this operator-pencil is self-adjoint and positive definite for sufficiently large negative values of the eigenparameter. Finally, it is established that the spectrum is discrete and the system of corresponding weak eigenfunctions forms an orthonormal basis of the appropriate Hilbert space. |
| Anahtar Kelimeler |
| Discontinuous Sturm–Liouville problems | eigenvalues | transmission conditions | weak eigenfunctions |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 17 |
| SCOPUS | 16 |
| Google Scholar | 19 |