Three nontrivial solutions for nonlinear fractional Laplacian equations
  We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three nonzero solutions. When the reaction term is sublinear at infinity, we apply the second deformation theorem and spectral theory. When the reaction term is superlinear at infinity, we apply the mountain pass theorem and Morse theory. 
Fatma Gamze D\"uzg\"un, Antonio Iannizzotto
math.AP