Higher-order Lidstone BVP And Nonoscillations For A Certain Funcional Differential System

This thesis, which is divided into four parts, is concerned with higher-order Lidstone boundary value problems(BVP) and nonoscillations for a certain funcional differential system.In the first part, the author studies the existence of at least three symmetric positive solutions for the Lidstone BVP of higher-order differential equations. A generalized fixed point theorem - the Five Functional Fixed Point Theorem - and some new techniques, which are different from the ordinary reasonings, show the main results.The second part solves the corresponding problems of higher-order difference equations. Especially, the definitions of Green's func-tions and their properties in the earlier papers are corrected and expressed here.In the third part, by applying some fixed point theorems and cone theory, the author obtains some sufficient and necessary conditions of the bounded and unbounded existence intervals of eigenvalues for certain higher-order discrete Lidstone BVP, respectively, under three different assumptions on the nonlinear term.The last part is concerned with the nonoscillatory problems of odd-dimentional systems of linear retarded functional differential equa-tions. Based upon the corresponding characteristic equations, the author gets some criteria for nonosillations by utilizing the matrix measures.