Existence Of Positive Solutions For Boundary Value Problems Of Two Types

In recent years,there has been considerable interest in the existence of positive solutions to boundary value problems of nonlinear ordinary differential equations.This thesis has mainly summarized some articles that studied the existence of positive solutions to boundary value problems of nonlinear ordinary differential equations in Chapter One.In the second chapter,we study the existence of positive solution to the nonlinear second-order two-point boundary value problem By constructing a cone P,define completely continuous operator T:P?P.According to the extended theorem of Leggett-Williams fixed point theorem,which respectively under expansion and compression conditions,we prove the existence of at least one positive solution to the above boundary value problem.In the third chapter,we study the existence of positive solution to the multi-point boundary problem where h:(0,1)?[0,+?)is continuous,h(x)is not identically equal to 0 and allows it singular at x = 0 and x = 1.By defining completely continuous operator A:P?P,according to the fixed point index we prove that the boundary value problem possesses at least one positive solution.