Pseudo Asymptotically Periodic Solutions for Volterra Difference Equations of Convolution Type

2019 ◽  
Vol 40 (4) ◽  
pp. 501-514
Author(s):  
Zhinan Xia
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Convolution Type ◽  
Asymptotically Periodic ◽  
Volterra Difference Equations ◽  
Asymptotically Periodic Solutions

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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