Non-resonant Fredholm alternative and anti-maximum principle for the   fractional $p-$Laplacian
  In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional $p-$Laplacian. The first result is a existence in a non-resonant range more specific between the first and second eigenvalue of the fractional $p-$Laplacian. The second result is the anti-maximum principle for the fractional $p-$Laplacian. 
Leandro M. Del Pezzo and Alexander Quaas
math.AP