AN INVERSE NODAL PROBLEM AND AMBARZUMYAN PROBLEM FOR THE PERIODIC $p$-LAPLACIAN OPERATOR WITH INTEGRABLE POTENTIALS

Abstract

In this note, we solve the inverse nodal problem and Ambarzumyanproblem for the $p$-Laplacian coupled with periodic or anti-periodicboundary conditions. We also extend some results in a previous paperto $p$-Laplacian with $L^1$ potentials, and for arbitrary linearseparated boundary conditions. There we prove a generalizedRiemann-Lebesgue Lemma which is of independent interest.