Existence Of Solutions For Boundary Value Problems Of Differential Equations Based On A Lower And Upper Solutions Approach

In this paper,we mainly study the existence of solutions for two-point boundary value problems and periodic boundary value problems of hyperplane systems in n-dimensional European space.In the first chapter,the research background and significance of boundary value problems of differential equations such as ordinary differential equation and partial differential equation are introduced.The research content and main conclusions of this paper are summarized.The second chapter on hyperplane system two-point boundary value problem,we only discuss the existence of system solutions in the case of well-ordered upper and lower solutions.We define the lower and upper solutions of the problem,and discuss the existence of the hyperplane system solutions under the boundary value conditions lA and lS which are "neither vertical line","not both vertical line" and“both vertical line”respectively.Theorem 2.5,Theorem 2.10 and Theorem 2.14 are the existence theorems of solutions of hyperplane systems under these three conditions respectively,and Claim 1～3 to prove the rationality of Theorem 2.5,Theorem 2.10 and Theorem 2.14.Finally,some inferences.The third chapter on hyperplane system periodic boundary value problem,We discuss two cases well-ordered and non-well-ordered upper and lower solution.The well-ordered upper and lower solutions we construct auxiliary problem,and prove fix problem(3.27)with no solution other than V,the topological degree parameter completes the proof of existence Theorem 3.5 of the solution of hyperplane system in this case.The Non-well-ordered upper and lower solution situation,we also give auxiliary problem and construct well-ordered upper and lower solution pairs,to prove the existence of the solution of this situation.The fourth chapter gives the summary and prospect.