Displaying similar documents to “On some constants in approximation by Bernstein operators.”

On the existence of solutions of some second order nonlinear difference equations

Małgorzata Migda, Ewa Schmeidel, Małgorzata Zbąszyniak (2005)

Archivum Mathematicum

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We consider a second order nonlinear difference equation Δ 2 y n = a n y n + 1 + f ( n , y n , y n + 1 ) , n ∈ N . ( E ) The necessary conditions under which there exists a solution of equation (E) which can be written in the form y n + 1 = α n u n + β n v n , are given. Here u and v are two linearly independent solutions of equation Δ 2 y n = a n + 1 y n + 1 , ( lim n → ∞ α n = α < ∞ and lim n → ∞ β n = β < ∞ ) . A special case of equation (E) is also considered.

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.