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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2021)   > Article

On the existence of solutions of a nonlocal biharmonic problem

Sur l’existence de solutions d’un problème biharmonique non local


Khaled Kefi
Northern Border University
Kingdom of Saudi Arabia



Published on 5 January 2021   DOI : 10.21494/ISTE.OP.2020.0581

Abstract

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This paper is concerned with the existence of an eigenvalue for a p(x)-biharmonic Kirchhoff problem with Navier boundary condition. Under some suitable conditions, we establish that any λ > 0 is an eigenvalue . The proofs combine variational methods with energy estimates. The main results of this paper improve and generalize the previous one introduced by Kefi and Rădulescu (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 439-463).

This paper is concerned with the existence of an eigenvalue for a p(x)-biharmonic Kirchhoff problem with Navier boundary condition. Under some suitable conditions, we establish that any λ > 0 is an eigenvalue . The proofs combine variational methods with energy estimates. The main results of this paper improve and generalize the previous one introduced by Kefi and Rădulescu (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 439-463).

p(x)-biharmonic Kirchhoff problem Navier boundary condition variational principle generalized Sobolev spaces

p(x)-biharmonic Kirchhoff problem Navier boundary condition variational principle generalized Sobolev spaces