We study the validity of the comparison and maximum principles and their relation with principal eigenvalues, for a class of degenerate nonlinear operators that are extremal among operators with one-dimensional fractional diffusion.
We prove existence results for the Lane-Emden type systemwhere B1 is the unitary ball in R N , N > max{2α, 2β}, ν is the outward pointing normal, α, β ∈ N, α, β ≥ 1 and (−∆) α = −∆((−∆) α−1 ) is the polyharmonic operator. A continuation method together with a priori estimates will be exploited. Moreover, we prove uniqueness for the particular case α = 2, β = 1 and p, q > 1.
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