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

2018/09/14 by Ahmed Youssfi, Youssfi, Ahmed, Mohamed Mahmoud Ould Khatri +1
Mathematics · #35D30 #35P30 #46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D30 #msc:35P30 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1809.05591

23 pages

arxiv created 2019/08/16 · arxiv updated 2019/08/19

Abstract

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 λ₀ and λ₁ with λ₀≤λ₁ such that λ₁ is an eigenvalue of the problem while any value λ<λ₀ cannot be so. By means of Harnack-type inequalities and a strong maximum principle, we prove the isolation of λ₁ on the right side. We emphasize that throughout the paper no Δ₂-condition is needed.

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