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

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    0357377 - MÚ 2011 RIV US eng J - Journal Article
    Řehák, Pavel
    Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations.
    Abstract and Applied Analysis. -, - (2011), s. 986343. ISSN 1085-3375
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : second order q-difference equation * asymptotic behavior * q-regularly varying sequence * Banach fixed point theorem
    Subject RIV: BA - General Mathematics
    Impact factor: 1.318, year: 2011

    We derive necessary and sufficient conditions for (some or all) positive solutions of the halflinear q-difference equation D-q(Phi(D(q)y(t))) + p(t)Phi(y(qt)) = 0, t is an element of {q(k) : k is an element of N-0} with q > 1, Phi(u) = vertical bar u vertical bar(alpha-1) sgn u with alpha > 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 -> infinity is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.
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