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Inverse nodal problem for p-Laplacian energy-dependent Sturm-Liouville equation

Hikmet Koyunbakan

Author Affiliations

Department of Mathematics, Firat University, Elazig, 23119, Turkey

Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

Boundary Value Problems 2013, 2013:272  doi:10.1186/1687-2770-2013-272

Published: 12 December 2013


In this study, the inverse nodal problem is solved for p-Laplacian Schrödinger equation with energy-dependent potential function with the Dirichlet conditions. Asymptotic estimates of eigenvalues, nodal points and nodal lengths are given by using Prüfer substitution. Especially, an explicit formula for a potential function is given by using nodal lengths. Results are more general than the classical p-Laplacian Sturm-Liouville problem. For the proofs, methods previously developed by Law et al. and Wang et al., in 2009 and 2011, respectively, are used. In there, they solved an inverse nodal problem for the classical p-Laplacian Sturm-Liouville equation with eigenparameter boundary conditions.

MSC: 34A55, 34L20.

Prüfer substitution; inverse nodal problem; p-Laplacian equation