Abstract
We consider a model Schrödinger operator with a constant coefficient on the unit segment and the Dirichlet and Neumann condition on opposite ends with a small translation in the free term. The value of the translation is small parameter, which can be both positive and negative. The main result is the spectral asymptotics for the eigenvalues and eigenfunctions with an estimate for the error term, which is uniform in the small parameter. For finitely many first eigenvalues and associated eigenfunctions we provide asymptotics in the small parameter. We prove that each eigenvalue is simple, and the system of eigenfunctions forms a basis in the space $L_2(0, 1).$
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
