EXISTENCE OF NONOSCILLATORY SOLUTIONS FOR SECOND-ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

In this work, an attempt is made to discuss the existence of nonoscillatory solutions of second order nonlinear neutral differential equations with variable delays. The main tools are Lebesgue’s dominated convergence theorem and Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions. This problem is considered in various ranges of the neutral coefficient. Further, two illustrative examples showing applicability of the new results are included.