Representation of solutions of difference equations with continuous time.

Péics, Hajnalka

Displaying similar documents to “Representation of solutions of difference equations with continuous time.”

Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

Ethiraju Thandapani, L. Ramuppillai (1998)

Archivum Mathematicum

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This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form $Δ (a_{n - 1} | Δ y_{n - 1} |^{α - 1} Δ y_{n - 1}) + F (n, y_{n}) = G (n, y_{n}, Δ y_{n}), n \in N (n_{0}) (E)$ where $α > 0$ . Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.

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

N. Parhi (2011)

Mathematica Bohemica

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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...