Abstract
We study boundary value problems on noncompact cycle-free graphs (i.e., trees) for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of the spectrum and analyze the inverse problem of reconstructing the coefficients of a differential equation on the basis of the so-called Weyl functions. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing the solution by the method of spectral mapping.
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Original Russian Text © V.A. Yurko, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1658–1666.
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Yurko, V.A. Inverse spectral problem for differential operator pencils on noncompact spatial networks. Diff Equat 44, 1721–1729 (2008). https://doi.org/10.1134/S0012266108120082
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DOI: https://doi.org/10.1134/S0012266108120082