Geodesic
Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients
Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 411-425

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We obtain sufficient conditions for every solution of the differential equation $$ [y(t)-p(t)y(r(t))]^{(n)}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t) $$ to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation $$ [y(t)-p(t)y(r(t))]^{(n)}+q(t)G(y(g(t)))=f(t) $$ when $q(t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.
We obtain sufficient conditions for every solution of the differential equation $$ [y(t)-p(t)y(r(t))]^{(n)}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t) $$ to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation $$ [y(t)-p(t)y(r(t))]^{(n)}+q(t)G(y(g(t)))=f(t) $$ when $q(t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.
DOI : 10.21136/MB.2009.140673
Classification : 34C10, 34C15, 34K40
Keywords: oscillatory solution; neutral differential equation; asymptotic behaviour 
Dix, Julio G.; Ghose, Dillip Kumar; Rath, Radhanath. Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients. Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 411-425. doi: 10.21136/MB.2009.140673
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