Maximum and anti-maximum principle for the fractional p-Laplacian with indefinite weights

Abstract

We establish some non-resonance results and maximum and anti-maximum principles for the following quasilinear non local problem involving the fractional p-Laplacian operator perturbed by an indefinite potential{(−Δp)su+V|u|p−2u=λm|u|p−2u+f in Ω,u=0 in RN﹨Ω. Here p∈(1,+∞), s∈(0,1), V and m are indefinite and sign-changing functions of Lr(Ω) with r>max⁡{N,Nsp}; f∈Lr(Ω) is such that f≥0 and f≢0 in the regular bounded domain Ω⊂RN.