Oscillation of third-order neutral differential equations with damping and distributed delay

Abstract

The present paper focuses on the oscillation of the third-order nonlinear neutral differential equations with damping and distributed delay. The oscillation of the third-order damped equations is often discussed by reducing the equations to the second-order ones. However, by applying the Riccati transformation and the integral averaging technique, we give an analytical method for the estimation of Riccati dynamic inequality to establish several oscillation criteria for the discussed equation, which show that any solution either oscillates or converges to zero. The results make significant improvement and extend the earlier works such as (Zhang et al. in Appl. Math. Lett. 25:1514-1519 2012). Finally, some examples are given to demonstrate the effectiveness of the obtained oscillation results.

Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation

“…For more results about neutral third-order functional differential equations, see, e.g., [13][14][15][16][17] and related references. For the recent advance in the theory and application of Mawhin's continuation theorem and periodic solutions, see [18][19][20].…”

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

“…Koplatadze [21], Wei [22], and Koplatadze et al [23] investigated the oscillation criterion of equation χ ( ) + q( )χ(σ( )) = 0, ≥ 0 , and obtained sufficient conditions for it to be oscillatory. Similarly, Bai [24] and Karpuz et al [25] discussed the oscillation criterion for the equation…”

Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions

“…Many researchers have intensively studied the topic of oscillation of fourth or higher order differential equations in depth, and many strategies for establishing oscillatory criteria for fourth or higher order differential equations have been developed. Several works, see [6][7][8][9][10][11][12][13][14][15][16][17][18], contain extremely interesting results linked to oscillatory features of solutions of neutral differential equations and damped delay differential equations with or without distributed deviating arguments.…”