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.

In this paper, we study the graph polynomial that records spanning rooted forests fG of a given graph. This polynomial has a remarkable reciprocity property. We give a new bijective proof for this theorem which has Prüfer coding as a special case.

We deal with an inverse nodal problem for p-Laplacian Sturm-Liouville equation which includes Coulomb type potential function under boundary condition depends on polynomial spectral parameter. Here, we get some asymptotic formulas of eigenvalues and nodal parameters by using a suitable Prüfer substitution. Eventually, we construct Coulomb potential by using nodal lengths. c ©2017 All rights res...