Solutions For The Systems Of Two Classes Nonlinear Differential Equations

In this paper, by using the fixed point theorem, the monotone iterative method, the principle of contraction mapping, cone expansion and contraction theory, we study the existence and multiplicity of solutions for the systems of first order nonlinear differential equations and the systems of second order nonlinear differential equations. Some new results are obtained, some relevant results are extended and improved. The structure of this paper as follows. In the first chapter, we introduce the background of the discussed problem of this thesis briefly, and we state the main results of this thesis concretely.The second chapter has two parts, In the first part, we investigate the systems of first order nonlinear differential equations with impulsive term. Where ( )f∈J×R+, R+, ( )g∈J×R+, R+,J =[0 .1].The sufficient conditions for the existence of solutions are obtained.In the second part, we investigate the systems of first order nonlinear integro-differential equations with impulsive termBy using the fixed point theorem, we obtain that the above IVP has a solution under some certain conditions.The third chapter also has two parts, In the first parts, we study the systems of second order nonlinear differential equations two-point boundary value problem where ( )g∈J×R+, R+, J =[0 .1] .By using the cone expansion and contraction theory, we obtain a new multi-solution theorem. In the second part, we investigate the systems of second order nonlinear differential equations two-point boundary value problem:By applying the monotone iterative method, we obtain that the above problem has a solution under some certain conditions.