Study On The Existence Of Solutions Of Boundary Value Of Two Kinds Of Nonlinear Differential Equations

Nonlinear differential equations play an important role in modern mathematical research.The important value of theoretical research is self-evident.In recent years,nonlinear differential equations,high order differential equations,singular boundary value problems and conjugate boundary value problems are the most active fields of analytical mathematics.Many researchers and scholars have made great achievements.Our work of this article is as follows:The first chapter of this paper introduces the background and significance of the study of this article,and it introduces and analyzes the status quo of research on the boundary value of nonlinear differential equations all over the world.In chapter 2,we study a class of 2n-order nonlinear singular boundary value problems and apply the fixed-point theorem on this problem.Under the nonlinear condition,we combine the appropriate conditions to obtain the symmetric positive solutions of the equation.The result of this article is to expand and improve some of the most recent results.In addition,new results are presented by giving a practical example.In chapter 3,we study a class of nonlinear fractional(n-1,1)conjugate boundary value problems with resonance,and apply Mawhin coincidence degree theory to this problem in terms of nonlinear conditions and integral boundary conditions tofurther study the existence of solutions.