Pasquale Candito

Infinitely many solutions for a class of discrete non-linear boundary value problems

The existence of infinitely many solutions for a discrete non-linear Dirichlet problem involving the p-Laplacian, under appropriate oscillating behaviours of the non-linear term, is established. The approach is based on the critical point theory.

INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES

In this paper, we establish the existence of infinitely many solutions to a Neumann problem involving the p-Laplacian and with discontinuous nonlinearities. The technical approach is mainly based on a very recent result on critical points for possibly non-smooth functionals in a Banach space due to Marano and Motreanu, namely Theorem 1.1 in a paper that is to appear in the journal J. Diff. Eqns (see Theorem 2.3 in the body of this paper). Some applications are presented. Throughout the sequel, Ω is a non-empty bounded open set of the real Euclidean space R n , n 3, with boundary of class C ∞ , a belongs to L ∞ (Ω), with ess inf Ω a> 0; α(x), β(x) lie in L 1 (Ω) with min{α(x) ,β (x)} 0 a.e. in Ω, and p ∈ )n, +∞(. Consider the

On a class of nonlinear variational–hemivariational inequalities

A three critical points theorem for nondifferentiable functions is pointed out and an existence result of multiple solutions for a Neumann elliptic variational–hemivariational inequality involving the p-laplacian is established. As an application, a Neumann problem for elliptic equations with discontinuous nonlinearities is studied.

Existence of Two Solutions for a Second-Order Discrete Boundary Value Problem

Abstract The existence of two nontrivial solutions for a class of nonlinear second-order discrete boundary value problems is established. The approach adopted is based on variational methods.

Variational Methods on Finite Dimensional Banach Spaces and Discrete Problems

Abstract In this paper, existence and multiplicity results for a class of second-order difference equations are established. In particular, the existence of at least one positive solution without requiring any asymptotic condition at infinity on the nonlinear term is presented and the existence of two positive solutions under a superlinear growth at infinity of the nonlinear term is pointed out. The approach is based on variational methods and, in particular, on a local minimum theorem and its variants. It is worth noticing that, in this paper, some classical results of variational methods are opportunely rewritten by exploiting fully the finite dimensional framework in order to obtain novel results for discrete problems.

Existence of solutions for a nonlinear algebraic system with a parameter

Abstract Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established. Our goal was achieved requiring an appropriate behavior of the nonlinear term f , either at zero or at infinity, without symmetry conditions. In addition, for a suitable class of systems, a strong discrete maximum principle is presented.

Nonlinear noncoercive Neumann problems with a reaction concave near the origin

We consider a nonlinear Neumann problem driven by the

2 -SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS

p

Nonlinear Difference Equations with Discontinuous Right-Hand Side

-Laplacian with a concave parametric reaction term and an asymptotically linear perturbation. We prove a multiplicity theorem producing five nontrivial solutions all with sign information when the parameter is small. For the semilinear case

TWO SOLUTIONS TO A NONLINEAR NEUMANN PROBLEM WITHOUT ASYMPTOTIC CONDITIONS

(p=2)