Elliptic perturbations for Hammerstein equations with singular nonlinear term

Abstract

We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the integral equation are proved. Moreover, these results are applied to nonlinear singular homogeneous Dirichlet problems.

Keywords

• Hammerstein integral equations
• existence of positive solutions
• singular nonlinear boundary value problems
• singular elliptic perturbations.