Existence of positive solutions to systems of nonlinear integral or differential equations

Abstract

In this paper, we are concerned with existence of positive
solutions for systems of nonlinear Hammerstein integral equations,
in which one nonlinear term is superlinear and the other is
sublinear. The discussion is based on the product formula of fixed
point index on product cone and fixed point index theory in cones.
As applications, we consider existence of positive solutions for
systems of second-order ordinary differential equations with
different boundary conditions.