An iterative method for the qualitative analysis of nonlinear neutral delay differential equations (Q6579983)

This paper concerns (i) oscillatory behavior of solutions of nonlinear neutral delay (and advanced) differential equation \N\[\N(x(t) - r(t)x(\alpha(t)))' + \sum_{i=1}^n s_i(t)H_i(x(\beta_i(t))) = 0, \tag{E} \N\] \Nwith deviating arguments; (ii) existence of bounded positive solutions of (E); (iii) the effect of delay terms on the behavior of solutions of (E). Oscillatory nature of solutions of (E) is studied by an iterative method. The existence and uniqueness of bounded positive solutions of (E) is given using Banach fixed point theorem. The effect of delay terms on the behavior of solutions of (E) is shown by means of employing MATLAB algorithms. These results extend the theory of (E), and provide a basic for further research on (E) and their applications. Authors give three examples to illustrate main results. Other problems remain open for solutions of (E) and nonlinear fractional delay differential equations with time-varying arguments.