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 ∈ RN is a bounded open set with sufficiently smooth boundary ∂Ω, p > 1, λ > 0, and f: Ω × R → R is a Carathéodory function satisfying the following condition: there exists t̄ > 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).

Walrasian competitive equilibrium, Quasi-variational inequality, 58E17, 58E35,

In this paper we deal with the existence of weak solutions for the following Neumann problemwhere ν is the outward unit normal to the boundary ∂Ω of the bounded open set Ω ⊂ R N . The existence of solutions, for the above problem, is proved by applying a critical point theorem recently obtained by B. Ricceri as a consequence of a more general variational principle.

Answering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/q) is decreasing in ]0, p*[ and Lipschitz continuous on compact subsets of ]0, p*[, λq being the p-th power of the best Sobolev constant for the embedding of W^(1,p)(O) into L^q(O

We study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of Kirchhoff typeHere, Ω is a bounded open set in R n with smooth boundary, a, b, λ are positive real numbers and f : R → R is a continuous function. In particular, we give an answer to an open problem recently proposed by B. Ricceri.