Geodesic
Oscillatory Behavior of Solutions of Certain Third-Order Mixed Neutral Functional Differential Equations
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 3
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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.
Classification : 34C10, 34K11, 39A21. 
@article{BMMS_2012_35_3_a1,
     author = {Zhenlai Han and Tongxing Li and Chenghui Zhang and Shurong Sun},
     title = {Oscillatory {Behavior} of {Solutions} of {Certain} {Third-Order} {Mixed} {Neutral} {Functional} {Differential} {Equations}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_3_a1/}
}
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AU  - Zhenlai Han
AU  - Tongxing Li
AU  - Chenghui Zhang
AU  - Shurong Sun
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JO  - Bulletin of the Malaysian Mathematical Society
PY  - 2012
VL  - 35
IS  - 3
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%A Chenghui Zhang
%A Shurong Sun
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%J Bulletin of the Malaysian Mathematical Society
%D 2012
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%U http://geodesic.mathdoc.fr/item/BMMS_2012_35_3_a1/
%F BMMS_2012_35_3_a1
Zhenlai Han; Tongxing Li; Chenghui Zhang; Shurong Sun. Oscillatory Behavior of Solutions of Certain Third-Order Mixed Neutral Functional Differential Equations. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2012_35_3_a1/