BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

The author studies the boundary value problems for systems of nonlinear second order differential difference equations and adopts a new-type Nagumo condition,in whichthe control function is a vector-valued function of several variables and which can guarantee simultaneoulsy and easily finding a priori bounds of each component of the derivatives of the solutions,Under this new-type Nagumo condition the existence results of solutions are proved by means of differential inequality technique.