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Youssef N. Raffoul 대한수학회 2018 대한수학회보 Vol.55 No.6
We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.
Positive Periodic Solutions of Systems of Functional Differential Equations
Youssef N. Raffoul 대한수학회 2005 대한수학회지 Vol.42 No.4
We apply a cone theoretic fixed point theorem and obtainconditions for the existence of positive periodic solutions of thesystem of functional differential equations $$ x'(t) = A(t)x(t) + \lambda f(t, x(t-\tau(t))
POSITIVE PERIODIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL DIFFERENTIAL EQUATIONS
RAFFOUL YOUSSEF N. Korean Mathematical Society 2005 대한수학회지 Vol.42 No.4
We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.
STABILITY IN FUNCTIONAL DIFFERENCE EQUATIONS USING FIXED POINT THEORY
Raffoul, Youssef N. Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.1
We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).
Raffoul, Youssef N. Korean Mathematical Society 2018 대한수학회보 Vol.55 No.6
We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.
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.