On Study For Existence Of Positive Solutions Of A Nonlinear Boundary Value Problem

In later years.all sorts of nonlinear problems have resulted from mathematics,physics, chemistry, biology, medicine, economics, engineering, cybernetics and so on. During the development of solving such problems,nonlinear functional analysis has been one of the most important research fields in modern mathematics. It mainly includes partial ordering method, topological degree method and the variational method.Also it provides a much effect theoretical tool for solving many nonlinear problems in the fields of the science and technology. And what is more , it is an importantapproach for studying nonlinear differential equations arising from many applied mathematics .L. E. J. Brouwerhad established the conception of topological degree for finite dimensional space in 1912.J.Lerry and J.Schauder had extend the conceptionto completely continous field of Banach. spacein 1934,afterward E.Rother, M. A. Kranoselskii, P. H. Rabinnowitz, H. Amann, K. Deimling had carried on embedded research on topological degree and cone theory. Many well known mathematicians in china, such as Zhang Gongqing,Guo Dajun,Chen Wenyuan, Sun Jingxian, and so on, has proud works in various fields of nonlinear functional annalysis[1-31].In this paper, we investigate the existence of positive solutions for the third- order third-point boundary value problem:λ＞0 is a parament,δ∈(0,1),η∈[1/2,1) arc constants. By Krasnoscl'skii fixed-pointtheorem,we can estabish some results on the existence of positive solutions of boundary value problem above.