Giovanni Anello

Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p -Laplacian

In this paper we present a result of existence of infinitely many arbitrarily small positive solutions to the following Dirichlet problem involving the p -Laplacian, where Ω ∈ R N is a bounded open set with sufficiently smooth boundary ∂Ω, p > 1, λ > 0, and f : Ω × R → R is a Caratheodory function satisfying the following condition: there exists t > 0 such that Precisely, our result ensures the existence of a sequence of a.e. positive weak solutions to the above problem, converging to zero in L ∞ (Ω).

A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption

This paper is focused on the investigation of the Walrasian economic equilibrium problem involving utility functions. The equilibrium problem is here reformulated by means of a quasi-variational inequality problem. Our goal is to give an existence result without assuming strong monotonicity conditions. To this end, we make use of a perturbation procedure. In particular, we will consider suitable perturbed utility functions whose gradient satisfies a strong monotonicity condition and whose associated equilibrium problem admits a solution. Then, we will prove that the limit solution solves the unperturbed problem. We stress out that our result allows us to consider a wide class of utility functions in which the Walrasian equilibrium problem may be solved.

On a Perturbed Dirichlet Problem for a Nonlocal Differential Equation of Kirchhoff Type

We study the existence of positive solutions to the following nonlocal boundary value problem in , on , where , is a Carathéodory function, is a positive continuous function, and is a real parameter. Direct variational methods are used. In particular, the proof of the main result is based on a property of the infimum on certain spheres of the energy functional associated to problem in , .

A note on a problem by Ricceri on the Ambrosetti-Rabinowitz condition

In this note we give an answer to Ricceris open problem involving the Ambrosetti-Rabinowitz superlinear condition.

Multiple nonnegative solutions for elliptic boundary value problems involving the

In this paper we present a result concerning the existence of two nonzero nonnegative solutions for the following Dirichlet problem involving the

p

p

-Laplacian

-Laplacian

Uniqueness of positive and compacton-type solutions for a resonant quasilinear problem

\cases -\Delta_p u=\lambda f(x,u) &\text{\rm in\ } \Omega,\\ u=0 &\text{\rm on\ } \partial \Omega, \endcases