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Inverse nodal problems for the -Laplacian with eigenparameter dependent boundary conditions. (English) Zbl 1235.34044

Summary: We study the issues of reconstruction of the inverse nodal problem for the one-dimensional \(p\)-Laplacian eigenvalue problem with eigenparameter boundary value conditions. A key step is the application of a modified Prüfer substitution to derive a detailed asymptotic expansion for the eigenvalues and nodal lengths. The parameter boundary data are also reconstructed.

MSC:

34A55 Inverse problems involving ordinary differential equations
34L05 General spectral theory of ordinary differential operators
34B09 Boundary eigenvalue problems for ordinary differential equations
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