ASYMPTOTIC PROPERTIES OF THIRD-ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY ARGUMENTS
R. Elayaraja, M. S. Kumar, and V. Ganesan
The present paper focuses on the oscillation and asymptotic properties of the third-order nonlinear neutral differential equations with variable delay arguments. By applying the Riccati transformation and the integral averaging technique, we give an analytical method for the estimation of Riccati differential inequality to establish several oscillation criteria for the discussed equation, which show that any solution either oscillates or converges to zero. We give several theorems and related examples to prove the significance of new theorems.
Keywords: Oscillation, non-linear, neutral differential equation, third order.