Reconstruction of discontinuous Sturm-Liouville pencils with the eigenvalue in the boundary condition on the half-line

Document Type : Original Article

Authors
Yasser Khalili 1
Abdolali Neamaty 2
1 Department of Basic Sciences, ‎Sari Agricultural‎ ‎Sciences and Natural Resources University, ‎578 Sari, ‎Iran
2 Department of Mathematics, ‎Faculty of Mathematical Sciences, ‎University of Mazandaran, Babolsar, ‎Iran
10.22034/maco.5.1.5
Abstract
This work considers the discontinuous differential pencil on the half-line with the spectral boundary condition. We establish some uniqueness theorems on the potentials for the Sturm-Liouville pencil by the incomplete inverse problem and the interior inverse problem methods. We  determine the potentials by only a set of eigenvalues knowing the coefficients $\beta_{0},\beta_{1},\beta_{2},\beta_{3}$ and potentials $q_{0}(x),q_{1}(x)$ on $(0,a).$ We also establish the potentials by a set of values of eigenfunctions at some internal point $x=a$ and eigenvalues.

Keywords

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