Displaying similar documents to “Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations”

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 ∈ 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.

Oscillation of forced nonlinear neutral delay difference equations of first order

N. Parhi, Arun Kumar Tripathy (2003)

Czechoslovak Mathematical Journal

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Necessary and sufficient conditions are obtained for every solution of Δ ( y n + p n y n - m ) ± q n G ( y n - k ) = f n to oscillate or tend to zero as n → ∞ , where p n , q n and f n are sequences of real numbers such that q n ≥ 0 . Different ranges for p n are considered.

Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order

N. Parhi, Anita Panda (2008)

Mathematica Bohemica

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In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form y n + 3 + r n y n + 2 + q n y n + 1 + p n y n = 0 , n ≥ 0 . These results are generalization of the results concerning difference equations with constant coefficients y n + 3 + r y n + 2 + q y n + 1 + p y n = 0 , n ≥ 0 . Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.