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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 \[ \Delta^p[x_n- cx_{n-l}]+ q_nf(x_{n-k})=h_n, \quad n\geq n_0, \] where \(\Delta\) is the forward difference operator \(\Delta x_n= x_{n+1}-x_n\), \(l\) and \(k\) are integers, \(c\neq\pm 1\) 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.

MSC:

39A11 Stability of difference equations (MSC2000)
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