Three solutions for a Neumann partial differential inclusion via   nonsmooth Morse theory
  We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the other negative). Then, by applying the nonsmooth Morse relation, we find a third non-zero solution. 
Francesca Colasuonno, Antonio Iannizzotto, Dimitri Mugnai
math.AP