Non-homogeneous Dirichlet problems with concave-convex reaction

The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous differential operator of p-Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a (p -1)-superlinear growth at infinity, provided that a behaviour less than (p -1)-linear of the nonlinear term in a suitable set is requested.

Hitting time distributions in different time windows in financial market

Three solutions for a Neumann boundary value problem involving the p-Laplacian

In this note we prove the existence of an open interval ]λ', λ"[ for each λ of which a Neumann boundary value problem involving the p-Laplacian and depending on λ admits at least three solutions. The result is based on a recent three critical points theorem.