Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

Ethiraju Thandapani; L. Ramuppillai

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Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations

N. Parhi (2011)

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In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form $Δ (p_{n - 1} Δ y_{n - 1}) + q y_{n} = 0, n \geq 1,$ where $q$ is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type $Δ (p_{n - 1} Δ y_{n - 1}) + q_{n} g (y_{n}) = f_{n - 1}, n \geq 1,$ where, unlike earlier works, $f_{n} \geq 0$ or $\leq 0$ (but $\neg \equiv 0)$ for large $n$ . Further, these results are...

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Oscillation of forced nonlinear neutral delay difference equations of first order

N. Parhi, Arun Kumar Tripathy (2003)

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Necessary and sufficient conditions are obtained for every solution of $Δ (y_{n} + p_{n} y_{n - m}) \pm q_{n} G (y_{n - k}) = f_{n}$ to oscillate or tend to zero as $n \to \infty$ , where $p_{n}$ , $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n} \geq 0$ . Different ranges for $p_{n}$ are considered.