Necessary And Sufficient Condition For The Existence Of Positive Solutions Of Nonlinear Second-Order Ordinary Differential Systems

In this paper, using the method of upper and lower solution in the nonlinear functional analysis and matching with monotone iteration, we study the necessary and sufficient conditionfor existence of the positive solution of two classes nonlinear ordinary differential system.The first chapter represents the problem's background and the evolution.In the second chapter, the following nonlinear seconder-order ordinary differential system with mixed boundary value condition is studiedBy constructing appropriate upper and lower solutions sequence, we obtained the necessaryand sufficient condition of the existence of the positive solution and proved the uniqueness of the solution; the convergence rate of the solution obtained by the monotone iteration method are computed. Furthermore, we proved that there exist a maximal solutionand a minimal solution between the upper solution and the lower solution which we constructed. The main tools are Schauder fixed point theorem, maximum principle and monotone iteration method.In the third chapter, the following second nonlinear second-order ordinary differential system is studied,Under appropriate hypothesis of the nonlinear term, by the upper and lower solution method, we also obtained two necessary and sufficient condition of the existence of positivesolution. The difficulty is to construct the appropriate upper and lower solution, the method we used can also discuss the existence of solution for the other differential system.