Positive Solutions Of Boundary Value Problems For Third-order Nonlinear Differential Equations In Banach Space

This master’s thesis consists of five parts,using the fixed point theorem,the fixed point index theory of conical map,Banach fixed point theorem and other methods,mainly studied the positive solution of the three-point boundary value problem of the third order differential equation in Banach space.The first part mainly introduces the background and present situation of boundary value problem of differential equation and the main work of this paper.The second part introduces the definitions and theorems involved in this paper.In the third part,using the fixed point exponent theory of conical mapping,we discuss the positive solution of the third-order three-point boundary value problem in Banach space when the nonlinear term contains only the first derivative term,and provide the conditions for the existence of positive solution.In the fourth part,by establishing a new cone and using the fixed point exponent theory of cone mapping,the positive solution of the third order three-point boundary value problem in Banach space is discussed when the nonlinear term contains all the derivatives,and the conditions for the existence of the positive solution are provided.In the fifth part,all the results are summarized,and the contents that need further study are prospected.