Khalili, YasserBaleanu, DumitruBaleanu, DumitruMatematik2022-12-072022-12-072020Khalili, Yasser; Baleanu, Dumitru (2020). "Recovering differential pencils with spectral boundary conditions and spectral jump conditions", Journal of Inequalities and Applications, Vol. 2020, No. 1.1029-242Xhttps://doi.org/10.1186/s13660-020-02537-zKhalili, Yasser/0000-0002-1402-8667In 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 is an element of (pi/2, pi) and parts of two spectra; (ii) if one boundary condition and the potentials qk(x) are prescribed on the interval [pi/2(1 - alpha), pi] for some alpha is an element of (0, 1), then parts of spectra S subset of sigma(L) are enough to determine the potentials q(k)(x) on the whole interval [0, pi] and another boundary condition.eninfo:eu-repo/semantics/openAccessInverse ProblemDifferential PencilSpectral Boundary ConditionSpectral Jump ConditionArticle2020110.1186/s13660-020-02537-z2-s2.0-85099514471WOS:000601171300001Q1Q2