Volume 35 • Number 3 • 2012   • Oscillatory Behavior of Solutions of Certain Third-Order Mixed Neutral Functional Differential Equations Zhenlai Han, Tongxing Li, Chenghui Zhang and Shurong Sun Abstract. The present work is concerned with the oscillation and asymptotic properties of the third-order mixed neutral differential equation $$ \left(a(t)\left(x(t)+p_1(t)x(t-\tau_1)+p_2(t)x(t+\tau_2)\right)''\right)'+q_1(t)x(t-\tau_3) +q_2(t)x(t+\tau_4)=0,\ \ \ t\geq t_0. $$ We establish two theorems which guarantee that every solution $x$ of the above equation oscillates or $\lim_{t\rightarrow\infty}x(t)=0$. These results complement some known results obtained in the literature. Some examples are considered to illustrate the main results. 2010 Mathematics Subject Classification: 34C10, 34K11, 39A21. Full text: PDF