Positive Solutions for Abstract Hammerstein Equations and Applications

Abstract

The authors use fixed point index properties to prove existence of positive solutions to the abstract Hammerstein equation $u=LFu$ where $L:E\rightarrow E$ is a compact linear operator, $F:K\rightarrow K$ is a continuous and bounded mapping, $E$ is a Banach space, and $K$ is a cone in $E$. The results obtained are used to prove existence results for positive solutions to two point boundary value problems associated with differential equations.