Inverse Nodal Problem for P-Laplacian energy-dependent Sturm-Liouville

TL;DR

This paper addresses the inverse nodal problem for a p-Laplacian energy-dependent Sturm-Liouville equation, providing asymptotic estimates and an explicit formula for the potential, extending classical results with more general conditions.

Contribution

It introduces a novel approach to solve the inverse nodal problem for energy-dependent p-Laplacian equations, including explicit potential formulas and generalized asymptotic estimates.

Findings

Explicit formula for potential function using nodal lengths

Asymptotic estimates of eigenvalues and nodal points

Results extend classical p-Laplacian Sturm-Liouville problems

Abstract

In this study, inverse nodal problem is solved for p-Laplacian Schr\"odinger equation with energy-dependent potential with the Drichlet conditions. Asymptotic estimates of eigenvalues, nodal points and nodal lengths are given by using Pr\"ufer substitution. Especially, an explicit formula for potential function is given by using nodal lengths. Results are more general than classical p- Laplacian Sturm Liouville problem. For the proofs, it is used the methods given in the references <cite>lav3</cite>, <cite>Wang</cite>.