scholarly journals Existence and Global Asymptotic Behavior of S -Asymptotically ω -Periodic Solutions for Evolution Equation with Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hong Qiao ◽  
Qiang Li ◽  
Tianjiao Yuan
Keyword(s):  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Compact Semigroup ◽  
Existence Results ◽  
Asymptotically Periodic ◽  
Abstract Evolution Equation ◽  
Equation With Delay ◽  
Asymptotically Periodic Solutions

This paper is concerned with the abstract evolution equation with delay. Firstly, we establish some sufficient conditions to ensure the existence results for the S -asymptotically periodic solutions by means of the compact semigroup. Secondly, we consider the global asymptotic behavior of the delayed evolution equation by using the Gronwall-Bellman integral inequality involving delay. These results improve and generalize the recent conclusions on this topic. Finally, we give an example to exhibit the practicability of our abstract results.

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.

Bounded solutions of nonlinear discrete volterra equations

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Małgorzata Migda ◽  
Janusz Migda
Keyword(s):  
Periodic Solutions ◽  
Volterra Equation ◽  
Sufficient Conditions ◽  
Volterra Equations ◽  
Real Constant ◽  
Bounded Solutions ◽  
All Solutions ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions

AbstractWe give sufficient conditions, under which for every real constant, there exists a solution of the nonlinear discrete Volterra equationconvergent to this constant. We give also conditions under which all solutions are asymptotically constant. Sufficient conditions for the existence of asymptotically periodic solutions of the above equation are also derived.

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.

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

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