Khalili, YasserBaleanu, Dumitru2022-12-072022-12-072020Khalili, Yasser; Baleanu, Dumitru (2020). "Recovering differential pencils with spectral boundary conditions and spectral jump conditions", Journal of Inequalities and Applications, Vol. 2020, No. 1.1025-5834http://hdl.handle.net/20.500.12416/5960In 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 qk(x) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point b∈(π2,π) and parts of two spectra; (ii) if one boundary condition and the potentials qk(x) are prescribed on the interval [π/ 2 (1 − α) , π] for some α∈ (0 , 1) , then parts of spectra S⊆ σ(L) are enough to determine the potentials qk(x) on the whole interval [0 , π] and another boundary condition.eninfo:eu-repo/semantics/openAccessDifferential PencilInverse ProblemSpectral Boundary ConditionSpectral Jump ConditionArticle2020110.1186/s13660-020-02537-z