Geodesic
Oscillation of solutions to third-order half-linear neutral differential equations
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we study the oscillation of solutions to the third-order neutral differential equations

$ \Big(a(t)\big([x(t)\pm p(t)x(\delta(t))]''\big)^\alpha\Big)' + q(t)x^\alpha(\tau(t)) = 0. $

Sufficient conditions are established so that every solution is either oscillatory or converges to zero. In particular, we extend the results obtain in [1] for $a(t)$ non-decreasing, to the non-increasing case.
Classification : 34K11, 34C10
Keywords: third-order neutral differential equation, Riccati transformation, oscillation of solutions 
@article{EJDE_2012__2012__a38,
     author = {Dzurina,  Jozef and Thandapani,  Ethiraju and Tamilvanan,  Sivaraj},
     title = {Oscillation of solutions to third-order half-linear neutral differential equations},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1243.34095},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a38/}
}
TY  - JOUR
AU  - Dzurina,  Jozef
AU  - Thandapani,  Ethiraju
AU  - Tamilvanan,  Sivaraj
TI  - Oscillation of solutions to third-order half-linear neutral differential equations
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
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LA  - en
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%A Dzurina,  Jozef
%A Thandapani,  Ethiraju
%A Tamilvanan,  Sivaraj
%T Oscillation of solutions to third-order half-linear neutral differential equations
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a38/
%G en
%F EJDE_2012__2012__a38
Dzurina,  Jozef; Thandapani,  Ethiraju; Tamilvanan,  Sivaraj. Oscillation of solutions to third-order half-linear neutral differential equations. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a38/