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Summary: Electronic Journal of Qualitative Theory of Differential Equations
2009, No. 16, 1-9; http://www.math.u-szeged.hu/ejqtde/
ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF SECOND
ORDER NEUTRAL QUANTUM EQUATIONS WITH MAXIMA
DOUGLAS R. ANDERSON AND JON D. KWIATKOWSKI
Abstract. In this study, the behavior of solutions to certain second order quantum
(q-difference) equations with maxima are considered. In particular, the asymptotic
behavior of non-oscillatory solutions is described, and sufficient conditions for os-
cillation of all solutions are obtained.
1. introduction
Quantum calculus has been utilized since at least the time of Pierre de Fermat [8,
Chapter B.5] to augment mathematical understanding gained from the more tradi-
tional continuous calculus and other branches of the discipline; see Kac and Cheung
[4], for example. In this study we will analyze a second order neutral quantum (q-
difference) equation
D2
q x(t) + p(t)x(q-k
t) + r(t) max
s{0,··· , }
x(q-s
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