Displaying similar documents to “Sufficient condition for the non-oscillation of the non-homogeneous linear n -th order differential equation”

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.