ON NEUTRAL DIFFERENTIAL EQUATIONS AND THE MONOTONE ITERATIVE METHOD

The application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving suffi- cient conditions which guarantee that such problems have solutions. This approach is new and to the Authors’ knowledge, this is the first paper when the monotone iterative method is applied to neutral first–order differential equations with deviating arguments. An example is given to illustrate theoretical results. One may apply a numerical method based on the proposed monotone iterative method to obtain a numerical solution of our problems.