On a nonlinear eigenvalue problem for generalized Laplacian in Orlicz–Sobolev spaces. (January 2020) - Youssfi, Ahmed; Khatri, Mohamed Mahmoud Ould
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 λ 0 and λ 1 with λ 0 ≤ λ 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.