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, -Delta(p)u = lambdaf(x, u) in Omega, u = 0 on partial derivativeOmega, where Omega epsilon R-N is a bounded open set with sufficiently smooth boundary partial derivativeOmega p > 1, lambda > 0, and f : Omega x R --> R is a Caratheodory function satisfying the following condition: there exists t > 0 such that sup(tepsilon[0,t]) f((.), t) epsilon L-infinity(Omega). Precisely, our result ensures the existence of a sequence of a.e. positive weak solutions to the above problem, converging to zero in L-infinity(Omega).