Existence of positive solutions of nonlinear second order Dirichlet problems perturbed by integral boundary conditions

Abstract

In this paper we study a second-order nonlinear perturbed Dirichlet problem with integral boundary conditions. We obtain the exact expression of the Green’s function related to the perturbed problem in terms of the Green’s function of the homogeneous Dirichlet problem. Moreover, we characterize the set of parameters where the Green’s function has constant sign (which, contrary to the homogeneous case, can be either positive or negative) on its square of definition. Finally, as an application, the existence of positive solutions is derived from fixed point theory applied to related operators defined on suitable cones in Banach spaces.