Year 2020, Volume 49 , Issue 4, Pages 1373 - 1382 2020-08-06

On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition

Emir Ali MARİS [1] , Sertaç GÖKTAŞ [2]


The spectral problem
\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]
\[y(0)=0, \quad y'(0)=\lambda(ay(1)+by'(1)),\]
is considered, where $\lambda$ is a spectral parameter, $q(x)\in{{L}_{1}}(0,1)$ is a complex-valued function, $a$ and $b$ are arbitrary complex numbers which satisfy the condition $|a|+|b|\ne 0$. We study the spectral properties (existence of eigenvalues, asymptotic formulae for eigenvalues and eigenfunctions, minimality and basicity of the system of eigenfunctions in ${{L}_{p}}(0,1)$) of the above-mentioned Sturm-Liouville problem.
eigenvalues, eigenfunctions, minimal system, basis
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-7620-8754
Author: Emir Ali MARİS
Institution: MERSIN UNIVERSITY
Country: Turkey


Orcid: 0000-0001-7842-6309
Author: Sertaç GÖKTAŞ (Primary Author)
Institution: MERSIN UNIVERSITY
Country: Turkey


Dates

Publication Date : August 6, 2020

Bibtex @research article { hujms479445, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1373 - 1382}, doi = {10.15672/hujms.479445}, title = {On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition}, key = {cite}, author = {Mari̇s, Emir Ali and Göktaş, Sertaç} }
APA Mari̇s, E , Göktaş, S . (2020). On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1373-1382 . DOI: 10.15672/hujms.479445
MLA Mari̇s, E , Göktaş, S . "On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1373-1382 <https://dergipark.org.tr/en/pub/hujms/issue/56305/479445>
Chicago Mari̇s, E , Göktaş, S . "On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1373-1382
RIS TY - JOUR T1 - On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition AU - Emir Ali Mari̇s , Sertaç Göktaş Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.479445 DO - 10.15672/hujms.479445 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1373 EP - 1382 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.479445 UR - https://doi.org/10.15672/hujms.479445 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition %A Emir Ali Mari̇s , Sertaç Göktaş %T On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.479445 %U 10.15672/hujms.479445
ISNAD Mari̇s, Emir Ali , Göktaş, Sertaç . "On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1373-1382 . https://doi.org/10.15672/hujms.479445
AMA Mari̇s E , Göktaş S . On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1373-1382.
Vancouver Mari̇s E , Göktaş S . On the spectral properties of a Sturm-Liouville problem with eigenparameter in the boundary condition. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1373-1382.