Geodesic
Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations
Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 11-27

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Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of \[ [y(t) - y(t-\tau )]^{(n)} + Q(t) G(y(t-\sigma )) = 0, \ t \ge 0, \tag $*$ \] where $n \ge 3$ is odd. Sufficient conditions are obtained for all solutions of $(*)$ to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with $(*)$ to oscillate or tend to zero as $t \rightarrow \infty $. In this case, there is no restriction on $n$.
Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of \[ [y(t) - y(t-\tau )]^{(n)} + Q(t) G(y(t-\sigma )) = 0, \ t \ge 0, \tag $*$ \] where $n \ge 3$ is odd. Sufficient conditions are obtained for all solutions of $(*)$ to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with $(*)$ to oscillate or tend to zero as $t \rightarrow \infty $. In this case, there is no restriction on $n$.
DOI : 10.21136/MB.2004.134104
Classification : 34C10, 34C15, 34K11, 34K40
Keywords: oscillation; nonoscillation; neutral differential equations 
Parhi, N.; Rath, R. N. Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations. Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 11-27. doi: 10.21136/MB.2004.134104
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