Asymptotic Behavior of Solutions to Half‐Linear q‐Difference Equations

Pavel Řehák

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: 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.

Date: 2011
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https://doi.org/10.1155/2011/986343

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:986343

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