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The existence of positive solutions and oscillation of solutions of higher-order difference equations with forcing terms. (English) Zbl 0933.39026
Summary: Sufficient conditions are established for the existence of positive solutions, and oscillation of all bounded solutions of the neutral difference equation $$\Delta^p[x_n- cx_{n-l}]+ q_nf(x_{n-k})=h_n, \quad n\ge n_0,$$ where $\Delta$ is the forward difference operator $\Delta x_n= x_{n+1}-x_n$, $l$ and $k$ are integers, $c\ne\pm 1$ is a real number, and $\{q_n\}$ and $\{h_n\}$ are real sequences. It is also shown that some of these sufficient conditions are necessary.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
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