Sub and supersolutions, invariant cones and multiplicity results for   p-Laplace equations
  For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient flow of enlarged cones in the $W^{1,p}_0$ topology. With this, we prove abstract existence and multiplicity theorems in the presence of variously ordered pairs of sub-supersolutions. As an application, we provide a four solutions theorem, one of the solutions being sign-changing. 
Maria-Magdalena Boureanu, Benedetta Noris and Susanna Terracini
math.AP