Abstract Operator Equations And Nonlinear Semi-regular Boundary Value Problem The Solution And Its Applications

Nonlinear functional analysis is an important branch of morderm analysis mathmatics, because it can explain all kinds of natural phenomenal, more and more mathematicans are devoting their time to it.Among them, the nonlinear integral equations , the nonlinear differential equations in Banach Spacethe and the nonlinear boundary value problem comes from a lot of branches of applied mathematics and physics, they are at present one of the most active fields that is studied in analyse mathematics. The present paper employs the cone theory, fixed point index theory, and Krasnoselskii fixed point theorem and so on, to investigate the existence of positive solutions of several classes of integral equations and differential equations singular boundary value problem. The obtained results are either new or intrinsically generalize and improve the previous relevant ones under weaker conditions. Most results of this paper are published or to appear in important journals of the world or China, for example, 《 Journal of Qufu Normal University 》 , 《 Journal of Engineering Mathematics 》 etc. The paper is divided into six sections according to contents.In the first Section, by using partial order method, the existence and uniqueness of solutions for systems of a class of abstract operator equations in Banach Spaces. The result obtained in this paper improve and unify many recent results。 we give two applications to the system of nonlinear integral equations and the systems of nonlinear differential equations in Banach Space, and we obtain the unique solution and interative sequences which converge unique solution and the error estimation.In the second section , by using the fixed point theory in cones, we obtained the existence of positive solutios for the third-order two-point semipositone...