Global L^∞ and Decay Estimate for Fractional p-Laplacian Equations in Ds,p( RN)

In this paper we present a new global L^∞ L ∞ -estimate for solutions u∈ Ds,p( RN) u ∈ D s , p ( R N ) of the fractional p -Laplacian equation u∈ Ds,p( RN): (-Δ ₚ)ˢ u=f(x,u) in RN, u ∈ D s , p ( R N ) : ( - Δ p ) s u = f ( x , u ) in R N , of the form u ∞≤ C Φ ( u β) ‖ u ‖ ∞ ≤ C Φ ( ‖ u ‖ β ) for some β > p β > p , where Φ : R⁺→ R⁺ Φ : R + → R + is a data independent function with lim s→ 0⁺Φ (s)=0 lim s → 0 + Φ ( s ) = 0 . The obtained