Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations - Pavel Řehák (Abstract and Applied Analysis)
We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear q-difference equation Dq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0, t∈{qk:k∈N0} with q>1, Φ(u)=|u|α−1sgn⁡u with α>1, to behave like q-regularly varying or q-rapidly varying or q-regularly bounded functions (that is, the functions y, for which a special limit behavior of y(qt)/y(t) as t→∞ is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.