Positive solutions of semi-Positone Hammerstein integral equations and applications

Multiple positive solutions for semi-positone Hammerstein integral equations are investigated. This provides a general framework for studying the existence of positive solutions for some semi-positone boundary value problems which can be transferred into the Hammerstein integral equations. We apply the new results on the existence of one or two positive solutions of the semi-positone integral equations to treat the semi-positone conjugate boundary value problems (BVPs) as illustrations although there are many other BVPs which can be treated in the similar way. We provide two explicit examples of semi-positone conjugate BVPs to exhibit applications of our results on the existence of one or two positive solutions.