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 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.