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On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators
- We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. (C) 2013 Elsevier Inc. All rights reserved.
| Author details: | Alexander ShlapunovORCiDGND, Nikolai Nikolaevich TarkhanovORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.jde.2013.07.029 |
| ISSN: | 0022-0396 |
| ISSN: | 1090-2732 |
| Title of parent work (English): | Journal of differential equations |
| Publisher: | Elsevier |
| Place of publishing: | San Diego |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2013 |
| Publication year: | 2013 |
| Release date: | 2017/03/26 |
| Tag: | Discontinuous Robin condition; Lipschitz domain; Non-coercive problem; Root function; Sturm-Liouville problem |
| Volume: | 255 |
| Issue: | 10 |
| Number of pages: | 33 |
| First page: | 3305 |
| Last Page: | 3337 |
| Funding institution: | Russian Foundation for Basic Research [11-01-91330-NNIO_a]; German Research Society (DFG) [TA 289/4-2] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
