Existence of positive continuous solutions of perturbed hammerstein equations

Abstract

We improve previous existence results for a class of perturbed Hammerstein integral equations, where the relevant Hammerstein operator is decreasing on positive functions. We strongly weaken the assumptions on the nonlinearities involved, and obtain existence of positive continuous solutions, even on noncompact domains, applying the Schauder-Tychonoff fixed-point theorem, via the generalized Ascoli theorem and the regularizing effect of the integral operator. An application to perturbed quadratic integral equations of interest in transport theory is also given

Keywords:

• Perturbed Hammerstein equations
• positive continuous solutions
• existence
• Schauder-Tychonoff fixed-point theorem
• perturbed quadratic integral equations