Study Of Positive Solutions To Boundary Value Problems For Differential Equations Of Two Kinds

The study of boundary value problems for ordinary differential equations has interested people for a long time. The existence of positive solutions of boundary value problems for nonlinear ordinary differential equations and systems draws close attention, in which the nonlinear function is endowed with the conditions of some different kinds in much literature.Firstly, we study the existence of positive solution for the second order m -point boundary value problem subject to the boundary value condition where (Lφ)(x)= (p(x)φ(x))+q(x)(φ)p(x),0<ξ1,<ξ2<…<ξm-2<1,ai∈[0,+∞), and h(x) is allowed to be singular at x= 0 and x= 1.The existence of positive solution is obtained for the m -point boundary value problem by means of the extended fixed point theorem concerning cone compression and expansion.Next, we study the existence of positive solution for the three order three-point boundary value problem subject to the boundary value condition Wherethe existence of positive solution is obtained in the paper for the three order three-point boundary value problem by means of the extended fixed point theorem concerning cone compression and expansion. In this thesis,the author applies the Avery Five Functional Fixed Point Theorem to obtain the existence of multiple positive solutions to the three order three-point boundary value problem.