Asymptotic Behavior of Solutions to Half‐Linear q‐Difference Equations
Copyright policy )Asymptotic Behavior of Solutions to Half‐Linear q‐Difference Equations
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.
- Academy of Sciences Library Czech Republic
- Institute of Mathematics Czech Republic
- Czech Academy of Sciences Czech Republic
- Academy of Science of the Czech Republic Czech Republic
- Academy of Sciences of the Czech Republic Czech Republic
positive solutions, Banach fixed point theorem, Difference equations, scaling (\(q\)-differences), QA1-939, Growth, boundedness, comparison of solutions to difference equations, asymptotic behavior, second order q-difference equation, q-regularly varying sequence, Mathematics, half-linear \(q\)-difference equation
positive solutions, Banach fixed point theorem, Difference equations, scaling (\(q\)-differences), QA1-939, Growth, boundedness, comparison of solutions to difference equations, asymptotic behavior, second order q-difference equation, q-regularly varying sequence, Mathematics, half-linear \(q\)-difference equation
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