Recovering differential pencils on compact graphs |
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Authors: | V. Yurko |
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Affiliation: | Department of Mathematics, Saratov University, Astrakhanskaya 83, Saratov 410026, Russia |
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Abstract: | We study boundary value problems on compact graphs without circles (i.e. on trees) for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate the inverse spectral problem of recovering the coefficients of the differential equation from the so-called Weyl vector which is a generalization of the Weyl function (m-function) for the classical Sturm-Liouville operator. For this inverse problem we prove the uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mappings. |
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Keywords: | 34A55 34B24 34L05 47E05 |
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