(untitled) (Nonlinear Studies, 2014)
In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem: equation* cases abla ( abla u^p-2 abla u) = f(x,u) + λ g(x,u) & in Ω u= 0 & on Ω, cases equation* where Ω ^N is an open bounded set with smooth boundary Ω and λ . Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and + ∞, our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space W_0^1,p(Ω) centered in the origin and with radius not dependent on λ.