Nonexistence of periodic solutions and S-asymptotically periodic solutions in fractional difference equations

2015 ◽  
Vol 257 ◽  
pp. 230-240 ◽  
Author(s):  
J. Diblík ◽  
M. Fečkan ◽  
M. Pospíšil
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions

Asymptotic behavior of mild solutions for nonlinear fractional difference equations

2018 ◽  
Vol 21 (2) ◽  
pp. 527-551 ◽  
Author(s):  
Zhinan Xia ◽  
Dingjiang Wang
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Difference Equations ◽  
Mild Solutions ◽  
Contraction Mapping Principle ◽  
Fractional Difference ◽  
Alternative Theorem ◽  
Fractional Difference Equations ◽  
Banach Contraction ◽  
Asymptotically Periodic

AbstractIn this paper, we establish some sufficient criteria for the existence, uniqueness of discrete weighted pseudo asymptotically periodic mild solutions and asymptotic behavior for nonlinear fractional difference equations in Banach space, where the nonlinear perturbation is Lipschitz type, or non-Lipschitz type. The results are a consequence of application of different fixed point theorems, namely, the Banach contraction mapping principle, Leray-Schauder alternative theorem and Matkowski’s fixed point technique.

scholarly journals Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Josef Diblík ◽  
Miroslava Růžičková ◽  
Ewa Schmeidel ◽  
Małgorzata Zbąszyniak
Keyword(s):  
Difference Equation ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Volterra Difference Equation ◽  
Asymptotically Periodic ◽  
Volterra Difference Equations ◽  
Asymptotically Periodic Solutions

A linear Volterra difference equation of the formx(n+1)=a(n)+b(n)x(n)+∑i=0nK(n,i)x(i),wherex:N0→R,a:N0→R,K:N0×N0→Randb:N0→R∖{0}isω-periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on∏j=0ω-1b(j)is assumed. The results generalize some of the recent results.

scholarly journals Existence of asymptotically periodic solutions of scalar Volterra difference equations

2009 ◽  
Vol 43 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Josef Diblík ◽  
Miroslava Růžičková ◽  
Ewa Schmeidel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Volterra Difference Equation ◽  
Asymptotically Periodic ◽  
Volterra Difference Equations ◽  
Asymptotically Periodic Solutions

Abstract There is used a version of Schauder’s fixed point theorem to prove the existence of asymptotically periodic solutions of a scalar Volterra difference equation. Along with the existence of asymptotically periodic solutions, sufficient conditions for the nonexistence of such solutions are derived. Results are illustrated on examples.

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