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| On a Class of Nonlinear Elliptic Problems involving the $\alpha(z)$-Biharmonic Operator with an $l(z)$-Hardy Term |
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| KeyWord:$\alpha(z)$-biharmonic operator, variable exponents, $l(z)$-Hardy term, Hardy-Rellich inequality, Mountain Pass Theorem |
| Author Name | Affiliation | | Aicha Oubaha | Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Technics, Sultan Moulay Slimane University, Beni Mellal, BP 523, 23000, Morocco | | Noureddine Moujane | Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Technics, Sultan Moulay Slimane University, Beni Mellal, BP 523, 23000, Morocco | | Mohamed El Ouaarabi | Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Technics, Sultan Moulay Slimane University, Beni Mellal, BP 523, 23000, Morocco
Mathematical Analysis, Algebra and Applications Laboratory, Faculty of Sciences A\"{i}n Chock, Hassan II University, Casablanca, BP 5366, 20100, Morocco | | Abderrahmane Raji | Applied Mathematics and Scientific Computing Laboratory, Faculty of Science and Technics, Sultan Moulay Slimane University, Beni Mellal, BP 523, 23000, Morocco |
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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 $\alpha(z)$-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. |
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