Solutions Of Several Classes Of Nonlinear Boundary Value Problems On The Half-line

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.The present paper employs the cone theory, fixed point index theory and the method of upper and lower solutions and so on, to investigate the existence of positive solutions of several classes of boundary value problems on the half-line and obtains some new results.The paper is divided into four chapters according to contents.In Chapter one, we mainly introduce the developing history of nonlinear functional analysis and some definitions.In Chapter two, we study the second-order differential equation on the half-line whereφ:(0,+∞)→(0,+∞),f:[0,+∞)×R2→R are continuous. By using the Sadovskii fixed point theorem, we get the existence of at least one (positive) solution. As an application, we give an example to demonstrate our results.In Chapter three, we give conditions on f involving pairs of upper and lower solutions which lead to the existence of at least three solutions of a second-order boundary value problem whereφ:R→R, is an increasing homeomorphism and positive homomor-phism andφ(0)=0.In Chapter four, by using monotone iterative technique, we study the existence of monotone iterative solutions for impulsive differential equations. Meanwhile we get the iterative theorem, and we give the iterative sequence.