Existence results for a Dirichlet boundary value problem through a local minimization principle

In this paper, a local minimum result for differentiable functionals is exploited in order to prove that a perturbed Dirichlet boundary value problem including a Lipschitz continuous non-linear term admits at least one non-trivial weak solution under an asymptotical behaviour of the nonlinear datum at zero. Some special cases and a concrete example of an application is then presented.