On Solvability Of A Second Order Nonlinear System Of Differential Equations

This paper investigate the second order nonlinear system of differential equationsThe first chapter states the importance of the study for the above system. When some nonlinear functions take special linear functions, the above system grows many cases of the study in [1-20]. However, under these cases of b (t ) =±1, q (t ) =±1 the above system is new and has been not discussed due to technical reasons in [1-20].The second chapter gives some related definitions.The third chapter with the aid of the Banach fixed point theorem and some natural modification of the technique in the literature, this paper establishes the existence results of uncountably many bounded positive solutions for the system of differential equations, put forward a few Mann type iterative approximation schemes and get several error estimates between the iterative approximations and the bounded positive solutions under these cases of b (t ) =±1 , q (t ) =±1 .The fourth chapter shows the feasibility and importance of the study through the application. Three nontrivial examples are presented to illuminate the main results. Through careful calculation and analysis, the feasibility of these condition of the main theorems is verified.