p⁢(x)p(x)-biharmonic operator involving the p⁢(x)p(x)-Hardy inequality-Reference-Cited by-同舟云学术

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

Published:2020-06-01 Issue:2 Volume:27 Page:233-247
ISSN:1572-9176
Container-title:Georgian Mathematical Journal
language:
Short-container-title:

Author:

El Khalil Abdelouahed¹,El Moumni Mostafa²,Morchid Alaoui Moulay Driss³,Touzani Abdelfattah³

Affiliation:

1. Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, 11623Riyadh, Saudi Arabia

2. Department of Mathematics, Faculty of Sciences El Jadida, University Chouaib Doukkali, P.O. Box 20, 24000El Jadida, Morocco

3. Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796Fez, Morocco

Abstract

AbstractIn 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

{\sup\Lambda=+\infty}

. Moreover, we prove that

{\inf\Lambda>0}

if and only if the domain Ω satisfies the

{p(x)}

-Hardy inequality.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/downloadpdf/journals/gmj/27/2/article-p233.xml

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