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p(x)-biharmonic operator involving the p(x)-Hardy inequality

  • Abdelouahed El Khalil , Mostafa El Moumni , Moulay Driss Morchid Alaoui EMAIL logo and Abdelfattah Touzani

Abstract

In this work, we investigate the spectrum denoted by Λ for the p(x)-biharmonic operator involving the Hardy term. We prove the existence of at least one non-decreasing sequence of positive eigenvalues of this problem such that supΛ=+. Moreover, we prove that infΛ>0 if and only if the domain Ω satisfies the p(x)-Hardy inequality.

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Received: 2015-10-11
Revised: 2016-12-09
Accepted: 2017-09-22
Published Online: 2018-03-23
Published in Print: 2020-06-01

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