Existence Of Positive Solutions For Boundary Value Problems Of Second Order Differential Equations With P(t)-Laplacian Operator

In this thesis,we mainly study the existence of positive solutions for boundary value problems of second order differential equations with p?t?-Laplacian operator.By using several types fixed point theorems,we present the sufficient conditions for the existence of positive solutions of different second order differential equation boundary value problems.In the first chapter,we briefly describe the research background,the research status and the main work of this paper.In the second chapter,we discuss the existence of positive solutions for a class of three-point boundary value problems with p?t?-Laplacian operator.In this chapter,we choose two different cones.By using the five-point functional fixed point theorem,we get the conclusion that three positive solutions exist at least for the boundary value problem,meanwhile there is an example to be given in the part.And by using Krasnosel'skill fixed point theorem,we obtain the existence theorem of the boundary value problem with two positive solutions at least.In the third chapter,when p(t)is a constant p,we study existence of pseudosymmetric positive solutions of Sturm-Liouville boundary value problems with p-Laplacian operator on time scales.By using Leggett-Williams fixed point theorem,we obtain the sufficient conditions for the existence of this boundary value problem with three positive solutions at least.By using the Avery-Henderson fixed point theorem,we get the existence theorem of the boundary value problem with two positive solutions at least.And it's also applied in an example at the same time.