Positive Solution For Multi-point BVPs With One-dimensional P-Laplacian

Nonlinear functional analysis are research discipline in analysis mathematics both to have the profound theory and to have the widespread application. It takes the nonlinear problems appearing in mathematics and the natural science as background to establish some general theories and methods to handle nonlinear problem. Since it can commendably explain many kinds of natural phenomena, in recent years, which has received widely attention in domestic and foreign mathematics and natural science field, and formed an important discipline gradually. To handle all kinds of nonlinear integral equations, the differential equations and the partial differential equations in actual problems, it plays role which can not be substituted.The dissertation is divided into three chapters:The first chapter introduces the background, methods of the related problems and the major work for this paper.The second chapter, by using the fixed point index theory and the fixed point theorem of cone expansion-compression of functional type, we firstly obtain some sufficient conditions of the existence of at least one, two positive solution for boundary value problems with the one-dimensional p-LaplacianBy means of Avery-Peterson fixed point theorem on cone and some skill and techniques of analysis, we consider the positive solutions for boundary value problems with the one-dimensional p-Laplacian. Some sufficient conditions of the existence of at least three positive solutions are obtained. the method can be extended to the study of 2m-point boundary value problem. Finally, our approach is based on the monotone iterative technique, studying the caseα=β,η= 1-ξ. Without the assumption of the existence of lower and upper solution, we obtain not only the existence of positive solutions for the problems (1),(2), but also establish iterative schemes for approximating the solutions.