<abstract xmlns="http://www.w3.org/1999/xhtml">This paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the <italic>p</italic>(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on <italic>C</italic>1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve <italic>μ</italic>1(λ) and also show that, the smallest curve <italic>μ</italic>1(λ) is positive for all 0 ≤ λ &lt; <italic>C</italic><italic>H</italic>, with <italic>C</italic><italic>H</italic> is the optimal constant of Hardy type inequality.</abstract>

This paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

Eigencurves of the <italic>p</italic>(·)-Biharmonic operator with a Hardy-type term

Laboratory LAMA Department of Mathematics Faculty of Sciences

Department of Mathematics and Statistics College of Science

Imam Mohammad Ibn Saud Islamic University (IMSIU)

AMNEA Group Department of Mathematics Faculty of Sciences and Technologies

Moroccan Journal of Pure and Applied Analysis

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

Eigencurves of the (·)-Biharmonic operator with a Hardy-type term

This paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a...

Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

Published Online: Oct 02, 2020

Page range: 198 - 209

Received: May 11, 2020

Accepted: Jul 06, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0015

Keywords
(·)-biharmonic operator, Variational methods, Ljusternik-Schnirelmann theory, (·)-Hardy’s inequality

© 2020 Mohamed Laghzal et al., published by Sciendo

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

Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

Published Online: Oct 02, 2020

Page range: 198 - 209

Received: May 11, 2020

Accepted: Jul 06, 2020

DOI: https://doi.org/10.2478/mjpaa-2020-0015

Keywords(·)-biharmonic operator, Variational methods, Ljusternik-Schnirelmann theory, (·)-Hardy’s inequality

© 2020 Mohamed Laghzal et al., published by Sciendo

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

Keywords
(·)-biharmonic operator, Variational methods, Ljusternik-Schnirelmann theory, (·)-Hardy’s inequality