Abstract
In this paper, we study a weighted eigenvalue problem of the degenerate operator associated with infinity Laplacian Δ∞hu+λa(x)|u|h−1u=0,inΩ,u=0,on∂Ω,where h>1,Δ∞hu=|Du|h−3Δ∞u is the h-homogeneous infinity Laplacian and a(x) is a positive continuous bounded function in Ω. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The approach to the weighted eigenvalue problem is based on the maximum principle and when a parameter is less than the principal eigenvalue, some existence and uniqueness results related to this problem are established.
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