Giuseppina D'Aguì

Three Solutions for a Discrete Nonlinear Neumann Problem Involving the -Laplacian

We investigate the existence of at least three solutions for a discrete nonlinear Neumann boundary value problem involving the -Laplacian. Our approach is based on three critical points theorems.

Multiplicity Results for a Perturbed Elliptic Neumann Problem

The existence of three solutions for elliptic Neumann problems with a perturbed nonlinear term depending on two real parameters is investigated. Our approach 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.

THREE NON-ZERO SOLUTIONS FOR ELLIPTIC NEUMANN PROBLEMS

In this note we obtain a multiplicity result for an eigenvalue Neumann problem. Precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three non-zero weak solutions.

Infinitely many solutions for a double Sturm---Liouville problem

In this paper, we prove the existence of infinitely many solutions to differential problems where both the equation and the conditions are Sturm–Liouville type. The approach is based on critical point theory.

Infinitely Many Solutions for Perturbed Hemivariational Inequalities

We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the -Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of infinitely many solutions. The main tool in order to obtain our abstract results is a recent critical-point theorem for nonsmooth functionals.

Constant sign solutions for parameter-dependent superlinear second-order difference equations

This paper studies the existence of constant sign solutions for a second-order parameter-dependent super linear difference equation. The approach is based on variational methods on finite dimensional Banach spaces.

Nonlinear noncoercive Neumann problems with a reaction concave near the origin

We consider a nonlinear Neumann problem driven by the

On the Neumann problem for elliptic equations involving the p-Laplacian

p

Three solutions to a perturbed nonlinear discrete Dirichlet problem

-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