arXiv subjects

Mohamed Mahmoud Ould Khatri

Publications and source records attributed to Mohamed Mahmoud Ould Khatri.

2 recordsLinked to original sources

arXiv2019

On a nonlinear eigenvalue problem for generalized Laplacian in Orlicz-Sobolev spaces

We consider a nonlinear eigenvalue problem for some elliptic equations governed by general operators including the $p$-Laplacian. The natural framework in which we consider such equations is that of Orlicz-Sobolev spaces. we exhibit two positive constants $λ_{0}$ and $λ_{1}$ with $λ_{0}\leqλ_{1}$ such that $λ_1$ is an eigenvalue of the problem while any value $λ<λ_{0}$ cannot be so. By means of Harnack-type inequalities and a strong maximum principle, we prove the isolation of $λ_{1}$ on the right side. We emphasize that throughout the paper no $Δ_2$-condition is needed.

math.AP↗

arXiv2018

Imbedding results in Musielak-Orlicz spaces with an application to anisotropic nonlinear Neumann problems

We prove a continuous embedding that allows us to obtain a boundary trace imbedding result for anisotropic Musielak-Orlicz spaces, which we then apply to obtain an existence result for Neumann problems with nonlinearities on the boundary associated to some anisotropic nonlinear elliptic equations in Musielak-Orlicz spaces constructed from Musielak-Orlicz functions on which and on their conjugates we do not assume the $Δ_2$-condition. The uniqueness is also studied.

math.AP↗