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Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

Ethiraju Thandapani, L. Ramuppillai (1999)

Kybernetika

In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form Δ 2 y n - 1 + q n y σ ( n ) γ = g n , where γ is a quotient of odd positive integers, in the superlinear case ( γ > 1 ) and in the sublinear case ( γ < 1 ) .

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

N. Parhi (2011)

Mathematica Bohemica

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 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 1 , where, unlike earlier works, f n 0 or 0 (but ¬ 0 ) for large n . Further, these results are used to obtain...

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