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Study on a Class of SturmLiouville Boudary Value Problems
Author: QianQingHua
Tutor: ShiPing
School: Nanjing University of Finance and Economics
Course: Applied Mathematics
Keywords: Nonlinear ordinary differential equation SturmLiouville boundary value problem Fixed point theorem Fixed point index Cone Positive solutions
CLC: O175.8
Type: Master's thesis
Year: 2011
Downloads: 12
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Abstract
In this thesis, we study mainly the existence of positive solutions of a class of SturmLiouville boundary value problems for second order singular nonlinear ordinary differential equations, by using the fixed point theorems in the cone theory . The paper is divided into three chapters, the content is the following :Chapter one is an introduction, first, it introduces briefly the background of generating nonlinear ordinary differential equation boundary value problems(BVP) and the methods and meanings of research on the BVP; then it summarizes the research situation of nonlinear ordinary differential equation boundary value problems in recent years, and research problems of the paper; finally , it mainly introduces the fundamental concepts as required , also it presents a fixed point theorem often applied in the paper by means of fixed point index in the cone theory and related results.In Chapter two , we study the existence of positive solutions of a class of second order singular nonlinear SturmLiouville twopoint boundary value problems under a new condition and show the existence of at least two positive solutions for this SturmLiouville boundary value problems .In Chapter three , we investigate the existence of positive solutions of second order singular nonlinear SturmLiouville multipoint boundary value problems and obtain the existence of at least two positive solutions for this class of second order singular SturmLiouville multipoint boundary value problems in which the nonlinear terms satisfy some new kind conditions.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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