The infimum eigenvalue for degenerate p(x)-biharmonic operator with the Hardy potentiel

Adnane Belakhdar; Hassan Belaouidel; Mohammed Filali; Najib Tsouli

doi:10.5269/bspm.62754

Adnane Belakhdar Mohammed First University https://orcid.org/0000-0002-2896-6873
Hassan Belaouidel Mohammed First University https://orcid.org/0000-0003-0770-2454
Mohammed Filali Mohammed First University
Najib Tsouli Mohammed First University

Abstract

The aim of this article is to study the existence of at least one unbounded nondecreasing sequence of nonnegative eigenvalues (λk)k≥1 for a class of elliptic Navier boundary value problems involving the degenerate p(·)-biharmonic operator with q(x)-Hardy inequality by using the variational technique based on the Ljusternik-Schnirelmann theory on C1-manifolds and the theory of the variable exponent Lebesgue spaces. Also, we obtain the positivity of the infimum eigenvalue for the problem.

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