The Existence Of Positive Solutions For A Class Nonlinear Constant Differential Equation With Integral Boundary Conditions

Differential equations are widely used in many disciplines and fields, and have made great achievements. Although the studies of differential equations with boundary value problems have made a series of results, the theoretical studies of many problems are not good enough. With the rapid development of boundary value problems, many new problems and new research directions emerge gradually. Depth studies of these issues are of great significance in both theory and practical application. Now, the studies of fractional differential equations receive more and more attention by scholars at home and abroad, especially the fractional order differential equations abstracted from practical problems are becoming mathematics research hot spots.In this paper, We mainly talk about the existence of positive solutions for a class nonlinear constant differential equation boundray value prolem with integral boundary conditions.The same questions are studied with some different methods.Firstly, by equivalent transformation, the boundary value problem can be changed into the integral equation, by which an abstract operator is constructed. Then by using the fixed-point therom on a proper cone, the existence of positive solutions can be obtained. Secondly, through the therom of iteration, the sequences can be obtained. So not only the existence of positive solutons can be obtained, but also the way how to get concrete solutions can be done. Furthermore, combining with numerical simulation, we show last results in form of tables and figures.