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Volume 7, Issue 5
On a Class of Nonlinear Elliptic Problems Involving the $α(z)$-Biharmonic Operator with an $l(z)$-Hardy Term

Aicha Oubaha, Noureddine Moujane, Mohamed El Ouaarabi & Abderrahmane Raji

DOI: 10.12150/jnma.2025.1870

J. Nonl. Mod. Anal., 7 (2025), pp. 1870-1885.

Published online: 2025-09

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  • Abstract

By applying the Mountain Pass Theorem, we establish the existence of a weak solution for a class of nonlinear elliptic problem involving an $α(z)$-biharmonic operator and with an $l(z)$-hardy term in a bounded domain of $\mathbb{R}^N.$ Provided that certain additional assumptions are made regarding the nonlinearities, the corresponding functional will satisfy the Palais-Smale condition.

  • Keywords

$α(z)$-biharmonic operator, variable exponents, $l(z)$-Hardy term, Hardy-Rellich inequality, Mountain Pass Theorem.

  • AMS Subject Headings

58E05, 35J60, 47J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1870, author = {Oubaha , AichaMoujane , NoureddineOuaarabi , Mohamed El and Raji , Abderrahmane}, title = {On a Class of Nonlinear Elliptic Problems Involving the $α(z)$-Biharmonic Operator with an $l(z)$-Hardy Term}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {5}, pages = {1870--1885}, abstract = {

By applying the Mountain Pass Theorem, we establish the existence of a weak solution for a class of nonlinear elliptic problem involving an $α(z)$-biharmonic operator and with an $l(z)$-hardy term in a bounded domain of $\mathbb{R}^N.$ Provided that certain additional assumptions are made regarding the nonlinearities, the corresponding functional will satisfy the Palais-Smale condition.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1870}, url = {http://global-sci.org/intro/article_detail/jnma/24395.html} }
TY - JOUR T1 - On a Class of Nonlinear Elliptic Problems Involving the $α(z)$-Biharmonic Operator with an $l(z)$-Hardy Term AU - Oubaha , Aicha AU - Moujane , Noureddine AU - Ouaarabi , Mohamed El AU - Raji , Abderrahmane JO - Journal of Nonlinear Modeling and Analysis VL - 5 SP - 1870 EP - 1885 PY - 2025 DA - 2025/09 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1870 UR - https://global-sci.org/intro/article_detail/jnma/24395.html KW - $α(z)$-biharmonic operator, variable exponents, $l(z)$-Hardy term, Hardy-Rellich inequality, Mountain Pass Theorem. AB -

By applying the Mountain Pass Theorem, we establish the existence of a weak solution for a class of nonlinear elliptic problem involving an $α(z)$-biharmonic operator and with an $l(z)$-hardy term in a bounded domain of $\mathbb{R}^N.$ Provided that certain additional assumptions are made regarding the nonlinearities, the corresponding functional will satisfy the Palais-Smale condition.

Oubaha , AichaMoujane , NoureddineOuaarabi , Mohamed El and Raji , Abderrahmane. (2025). On a Class of Nonlinear Elliptic Problems Involving the $α(z)$-Biharmonic Operator with an $l(z)$-Hardy Term. Journal of Nonlinear Modeling and Analysis. 7 (5). 1870-1885. doi:10.12150/jnma.2025.1870
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