Existence And Uniqueness Of Solutions For Several Types Of Boundary Value Problem Of Differential Equations

Differential equations are widely used in natural science and practical engineering,and their boundary value problem has become one of the hot spots in nonlinear science.The existence and uniqueness of the solutions of boundary value problems of several kinds of differential equations are considered in this paper,including the rotation period problem of the second order differential equation,the boundary value problem of the Caputo fractional differential iterative equation and the boundary value problem of the Riemann-Liouville fractional differential iterative equation.First of all,she introduce the research progress and social value of differential equations and related boundary value problems,and briefly describe some symbols and lemmas used in this paper.Next,propose a integrable solution of rotation period for the first time,and prove that the existence and uniqueness of the solution are obtained by Leray-Schauder fixed point theorem and truncation technique under non-resonant conditions when the rotation period belongs to different ranges.And then she use Leray-Schauder fixed point theory,Arzela-Ascoli theorem,and topological degree principle to study the existence and uniqueness of boundary value problem solutions for a class of Caputo fractional differential iterative equations with nonlinear terms under unilateral Lipschtiz conditions.Finally,due to the harsh boundary conditions of Riemann-Liouville fractional differential iterative equations,it is difficult to deal with this fractional differential iterative equation.Therefore,she prove the existence and uniqueness of the solutions of this kind of differential equations by introducing Green's function and constructor space.