Displaying similar documents to “Nonoscillatory half-linear difference equations and recessive solutions.”

Asymptotic properties for half-linear difference equations

Mariella Cecchi, Zuzana Došlá, Mauro Marini, Ivo Vrkoč (2006)

Mathematica Bohemica

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Asymptotic properties of the half-linear difference equation Δ ( a n | Δ x n | α s g n Δ x n ) = b n | x n + 1 | α s g n x n + 1 ( * ) are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to ( * ) are considered too. Our approach is based on a classification of solutions of ( * ) and on some summation inequalities for double series, which can be used also in other different contexts.

Oscillation of third-order half-linear neutral difference equations

Ethiraju Thandapani, S. Selvarangam (2013)

Mathematica Bohemica

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Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form Δ ( a n ( Δ 2 ( x n + b n x n - δ ) ) α ) + q n x n + 1 - τ α = 0 and Δ ( a n ( Δ 2 ( x n - b n x n - δ ) ) α ) + q n x n + 1 - τ α = 0 are established. Some examples are presented to illustrate the main results.