TY - JOUR AU - Khalili, Yasser AU - Baleanu, Dumitru PY - 2020 DA - 2020/12/22 TI - Recovering differential pencils with spectral boundary conditions and spectral jump conditions JO - Journal of Inequalities and Applications SP - 262 VL - 2020 IS - 1 AB - In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: $(i)$the potentials $q_{k}(x)$and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point $b\in (\frac{\pi }{2},\pi )$and parts of two spectra; $(ii)$if one boundary condition and the potentials $q_{k}(x)$are prescribed on the interval $[\pi /2(1-\alpha ),\pi ]$for some $\alpha \in (0, 1)$, then parts of spectra $S\subseteq \sigma (L)$are enough to determine the potentials $q_{k}(x)$on the whole interval $[0, \pi ]$and another boundary condition. SN - 1029-242X UR - https://doi.org/10.1186/s13660-020-02537-z DO - 10.1186/s13660-020-02537-z ID - Khalili2020 ER -