University of KashanMathematics Interdisciplinary Research2538-36397120220301Incomplete and Interior Inverse Problem for a Discontinuous Differential Pencil with the Spectral Boundary Condition on the Half-Line778711193610.22052/mir.2022.243155.1314ENYasser KhaliliDepartment of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, 578 Sari, Iran0000-0002-1402-8667Abdolali NeamatyDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranJournal Article20211003Differential pencils on the half-line with a spectral boundary condition having a discontinuity in an interior point are investigated. We prove two uniqueness theorems: (i) knowing <em>β</em><sub>1</sub> ,<em>β</em><sub>0</sub> and potentials <em>p</em>,<em>q</em> on (0,<em>a</em>), only eigenvalues suffice to determine the boundary value problem <em>B</em>. (ii) some in formation on eigenfunctions at <em>x</em> = <em>a </em>and eigenvalues establish the boundary value problem <em>B</em>.https://mir.kashanu.ac.ir/article_111936_a16d3692d646ee0022587c4862051b46.pdf