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PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY
Mariette R. Maroun,Youssef N. Raffoul 대한수학회 2005 대한수학회지 Vol.42 No.2
We use Krasnoselskii's ¯xed point theorem to show that the nonlinear neutral di??erence equation with delay x(t + 1) = a(t)x(t) + c(t)¢x(t ¡ g(t)) + q¡t; x(t); x(t ¡ g(t)¢ has a periodic solution. To apply Krasnoselskii's ¯xed point theo-rem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.
PERIODIC SOLUTIONS IN NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH FUNCTIONAL DELAY
MAROUN MARIETTE R.,RAFFOUL YOUSSEF N. Korean Mathematical Society 2005 대한수학회지 Vol.42 No.2
We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.