Existence Of Solutions For The Boundary Value Problems Of Kinds Of Differential Equations Under Barrier Strip Conditions

As is known to all,many engineering and scientific problems can be transformed into the research on the existence of solutions to the boundary value problems of differential equations,so our research has practical significance.This thesis mainly focuses on the existence of solutions for boundary value problem of several kinds of integer and conformable fractional differential equations and the existence results of solutions are given,the main methods are based on the Leray-Schauder nonlinear alternative theorem and the topological degree theorem.According to the content,this thesis is laid out as follows:In the first chapter,we introduce the research background,current situation and the significance of several kinds of integer and fractional differential equations.Besides,the main work of the full text and innovation points can be found as well.In the second chapter,we are devoted to study the existence of solutions for some two-point conformable fractional boundary value problems.Under the assumption where the nonlinear term f satisfy some certain conditions,some properties of conformable fractional derivatives and Leray-Schauder nonlinear alternative theorem are combined to obtain the existence results of solutions.And at the end of the chapter,an example is given to demonstrate the main results.In the third chapter,the solvability for some three-point boundary value problems of fourth order differential equation is considered.As is known to all,the fourth-order equations are widely used in many fields such as bridges and building construction.Similar to the second chapter,the existence result for the problems can be reached by making use of the Leray-Schauder nonlinear alternative theorem.Finally,two examples are given to demonstrate the main results.In the fourth chapter,we research the existence theorems for some nonlinear three-point boundary value problems with φ-Laplacian and the existence results are obtained.The research method is mainly based on the barrier strip technique and the topological degree theorem.In the end,two examples are given to demonstrate the main results.The fifth chapter makes a summary of the main contents of the full-text study and explained the practical meaning of the corresponding conclusions and will carry on the prospect to the future work.