Nonoscillatory solutions of neutral dynamic equations with positive and negative coefficients on time scales

Abstract

In this paper, we establish the existence of nonoscillatory solutions to neutral dynamic equations with positive and negative coefficients on time scales of the form
\begin{displaymath}
(x(t)-{\int_a^b p(t,\tau{})x(g(t,\tau{}))\Delta{}\tau{}})^\Delta{}+{\sum_{i=1}^l r_{i}(t)x(\delta_{i}(t))}-{\sum_{j=1}^m s_{j}(t)x(\eta_{j}(t))}=0.
\end{displaymath}
Two examples are included to illustrate our presented results. In our approaches, a key role is played by the fixed point technique.