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June  2007, 6(2): 441-451. doi: 10.3934/cpaa.2007.6.441

Positive solutions of semi-Positone Hammerstein integral equations and applications

K. Q. Lan 1,

1. 

Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada

Received  April 2006 Revised  November 2006 Published  March 2007

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.
Keywords: cone., multiple positive solutions, Hammerstein integral equation, Semi-positone, conjugate boundary value problem.
Mathematics Subject Classification: Primary: 34B18; Secondary: 34B15, 34B16, 47H10, 47H3.
Citation: K. Q. Lan. Positive solutions of semi-Positone Hammerstein integral equations and applications. Communications on Pure & Applied Analysis, 2007, 6 (2) : 441-451. doi: 10.3934/cpaa.2007.6.441
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