Roberto Livrea

Multiplicity theorems for the Dirichlet problem involving the p-Laplacian

Abstract In this paper, we establish some results on the existence of at least three weak solutions for Dirichlet problems involving the p -Laplacian by a variational approach.

Infinitely many periodic solutions for a second-order nonautonomous system

In this paper we are interested in multiplicity results for a second-order nonautonomous system. Infinitely many solutions follow from a recent variational principle by B. Ricceri.

2 -SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS

In this paper, some min-max theorems for even and C 1 functionals established by Ghoussoub are extended to the case of functionals that are the sum of a locally Lipschitz continuous, even term and a convex, proper, lower semi-continuous, even function. A class of non-smooth functionals admitting an unbounded sequence of critical values is also pointed out.

Nonlinear Difference Equations with Discontinuous Right-Hand Side

A discrete nonlinear problem involving the p−Laplacian and with a discontinuous right-hand side is studied. The existence of a precise open interval of positive eigenvalues, for which it admits at least three solutions, is established. The approach adopted is fully based on the variational methods developed in [14, 15] for non-smooth functions.