The authors deal with the existence of positive solutions to a second-order differential equation of the form (1): with suitable boundary conditions and . The function is supposed to satisfy either and or and for suitable and .
The main idea is to change (1) into a Hammerstein integral equation of the form . The compactness of is proved. This allows one to apply fixed point index theory for compact maps.
Two applications are given: the existence of eigenvalues to the equation and the existence of positive radial solutions to the equation .