<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>In this short paper, we give the proof of the Ambarzumyan theorem by zeros of eigenfunctions (nodal points) different from eigenvalues for the one-dimensional <italic>p</italic>-Laplacian eigenvalue problem. We show that the potential function <italic>q</italic>(<italic>x</italic>) is zero if the spectrum is in the specific form. We consider this theorem for <italic>p</italic>-Laplacian equation with periodic and anti-periodic cases. If <italic>p </italic>= 0, results are coincided with the results given for Sturm-Liouvile problem.</p>
</abstract>

In this short paper, we give the proof of the Ambarzumyan theorem by zeros of eigenfunctions (nodal points) different from eigenvalues for the one-dimensional p-Laplacian eigenvalue problem. We show that the potential function q(x) is zero if the spectrum is in the specific form. We consider this theorem for p-Laplacian equation with periodic and anti-periodic cases. If p = 0, results are coincided with the results given for Sturm-Liouvile problem.

Ambarzumyan theorem by zeros of eigenfunction

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Ambarzumyan theorem by zeros of eigenfunction"}

In this short paper, we give the proof of the Ambarzumyan theorem by zeros of eigenfunctions (nodal points) different from eigenvalues for the one-dimensional...

Ambarzumyan theorem by zeros of eigenfunction

Publié en ligne: 13 sept. 2023

Pages: 211 - 216

Reçu: 20 juin 2023

Accepté: 10 août 2023

DOI: https://doi.org/10.2478/ijmce-2023-0017

Mots clés
Ambarzumyan theorem, -Laplacian, spectrum

© 2023 Beyhan Kemaloglu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Ambarzumyan theorem by zeros of eigenfunction

Publié en ligne: 13 sept. 2023

Pages: 211 - 216

Reçu: 20 juin 2023

Accepté: 10 août 2023

DOI: https://doi.org/10.2478/ijmce-2023-0017

Mots clésAmbarzumyan theorem, -Laplacian, spectrum

© 2023 Beyhan Kemaloglu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Ambarzumyan theorem, -Laplacian, spectrum