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Keywords:
Third order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions
Third order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions
Summary:
In this paper we consider the equation \[y^{\prime \prime \prime } + q(t){y^{\prime }}^{\alpha } + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty )$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.
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