Displaying similar documents to “Second order linear difference equations over discrete Hardy fields”

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 and nonoscillation of second order neutral delay difference equations

Ethiraju Thandapani, K. Mahalingam (2003)

Czechoslovak Mathematical Journal

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Some new oscillation and nonoscillation criteria for the second order neutral delay difference equation Δ ( c n Δ ( y n + p n y n - k ) ) + q n y n + 1 - m β = 0 , n ≥ n 0 where k , m are positive integers and β is a ratio of odd positive integers are established, under the condition ∑ n = n 0 ∞ 1 c n < ∞ .