TY  - JOUR
ID  - Grace2015
LB  - Grace2015
AU  - Grace, Said R.
TI  - Oscillation criteria for third order nonlinear delay differential equations with damping
ST  - Oscillation criteria for third order nonlinear delay differential equations with damping
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 4
SP  - 485
EP  - 497
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.4.485
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.4.485
AB  - This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \[\left( r_{2}(t)\left( r_{1}(t)y^{\prime}(t)\right)^{\prime}\right)^{\prime}+p(t)y^{\prime}(t)+q(t)f(y(g(t)))=0.\tag{\(\ast\)}\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation \((\ast)\) oscillates or converges to zero, provided that the second order equation \[\left( r_{2}(t)z^{\prime }(t)\right)^{\prime}+\left(p(t)/r_{1}(t)\right) z(t)=0\tag{\(\ast\ast\)}\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation \((\ast)\) oscillates if equation \((\ast\ast)\) is nonoscillatory. We also establish results for the oscillation of equation \((\ast)\) when equation \((\ast\ast)\) is oscillatory.
KW  - oscillation
KW  - third order
KW  - delay differential equation
SN  - 1232-9274
ER  -