The Application Of Functional Theory In Integro-Differential Equations

In this thesis, we investigate the second order integro-differential equations. The main research includes three aspects: the initial value problem (IVP), the two-point boundary value problem (BVP) and the periodic boundary value problem (PBVP).By using the upper and lower solutions method and monotone iterative technique, we obtain the existence of the maximal and minimal solutions and the iterative sequence of corresponding solutions for the Integro-differential equations. In this thesis, we establish new comparison results and the results obtained generalize and improve the results corresponding to those obtained by others.The thesis is divided into five chapters according to contents. The first chapter is a preface. In the second and the third chapter, the IVP and BVP for second-order integro-differential equations are investigated. In the fourth chapter, we investigate the PBVP for second-order integro-differential equations and this problem includes two aspects: without u′item and with u′item. The last chapter is the summary of this thesis.