On the Positive Solutions of Discrete Equations in Infinite Interval

A b s t a r c t The following difference equation ∆u(k)+∑_(i=1)^m▒〖p_i (k)u(τ_i 〗(k))=0 are considered, where ∆u(k)=u(k+1)-u(k),p_(i ):N →R_+,τ_i:N→N,τ_i (k)≤k-1 for kϵN and lim┬(k→+∞)⁡〖τ_i (k)〗=+∞ (i=1,…,m). In the work sufficient conditions are established for all solutions of the above equation to be oscillatory.

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