Julio G. Dix, Department of Mathematics, Texas State University, San Marcos TX 78666, USA, e-mail: julio@txstate.edu; Dillip Kumar Ghose, Department of Mathematics, S. K. C. G. College, Paralakimidi, Dt Ganjam, Orissa, India, e-mail: dillip.math@gmail.com; Radhanath Rath, Department of Mathematics, Veer Surendra Sai University of Technilogy, Burla, Dist: Sambalpur, Orissa, India, 768018, e-mail: radhanathmath@yahoo.co.in
Abstract: 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.
Keywords: oscillatory solution, neutral differential equation, asymptotic behaviour
Classification (MSC 2000): 34C10, 34C15, 34K40
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