Could you advise me about how to define oscillation conditions for sum-difference equation of Volterra type y(n) = a(n) + sum(b(n-k)*y(k)) at k = 1, ..., n-1?
Article Asymptotic behavior and oscillation of difference equations ...
The attached paper to your question contains some sufficient conditions for the oscillation of the equation (when m=0 in the paper). So what do you mean? do you ask for more general or better conditions?
Thank you for your answer. I have f(n,u) = y(n). Then f(n,u) is increasing with respect to u. So, Condition (i) of Theorem 1 is valid. But Condition (g) of Theorem 4 is not valid: lim sum(h(n)) -> c >0. Thus, I can’t find a sufficient condition for oscillations.
Dear Igor, I suggest you the following book for the information on linear stability analysis for discrete equations: Yu. Kuznetsov, Elements of Applied Bifurcation Theory.
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