Positive Solutions Of Two-point Boundary Value Problems For Fourth-order Differential Equations

This pater is devoted to investigate positive solutions of the fourth-order two-point boudary value problems. This class of problems is used to describle the beam equation in engineering.Chapter1is the introduction of this paper, which introduces the present situation about this question.In chaper2, the existence of positive soutions for fourth-order two-point boundary value problem is considered, where h(x) allowed to be singular at both x=0and x=1. f:[0,+∞)â†'[0,+∞) is continuous. The problem is investigatigated by using the fixed point index theory and the conclutions of existing two positive solutions are obtained. The conclusions extend and improve the main results of Sun Jingxian and others.In chaper3, the existence of positive soutions for fourth-order two-point boundary value problem which containsφ" is considered, where The problem is investigatigated by using the fixed point index theory and the conclutions of existing two positive solutions are obtained. The conclusions extend and improve the main results of Pang Changci and others.