Existence of Bounded Solutions of Nonlinear Difference Equations in Banach Spaces

2014 ◽  
Vol 198 (3) ◽  
pp. 252-259
Author(s):  
I. M. Hrod
Keyword(s):  
Banach Spaces ◽  
Difference Equations ◽  
Bounded Solutions ◽  
Nonlinear Difference Equations

scholarly journals Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

2005 ◽  
Vol 2005 (17) ◽  
pp. 2769-2774
Author(s):  
Anna Kisiolek ◽  
Ireneusz Kubiaczyk
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Difference Equations ◽  
Measure Of Noncompactness ◽  
Nonlinear Difference Equations ◽  
Measure Of Weak Noncompactness ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

We consider the second-order nonlinear difference equations of the formΔ(rn−1Δxn−1)+pnf(xn−k)=hn. We show that there exists a solution(xn), which possesses the asymptotic behaviour‖xn−a∑j=0n−1(1/rj)+b‖=o(1),a,b∈ℝ. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988). We suppose thatfhas values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

scholarly journals QUALITATIVE BEHAVIOURS OF A SYSTEM OF NONLINEAR DIFFERENCE EQUATIONS

2021 ◽  
Vol 21 (1) ◽  
pp. 39-56
Author(s):  
ERKAN TAŞDEMİR ◽  
YÜKSEL SOYKAN
Keyword(s):  
Real Number ◽  
Difference Equations ◽  
Equilibrium Points ◽  
Bounded Solutions ◽  
Nonlinear Difference Equations ◽  
Related System ◽  
Numerical Examples ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Theoretical Results

The paper aims to study the dynamics of a system of nonlinear difference equations x_(n+1)=x_(n-1) y_n+A,y_(n+1)=y_(n-1) x_n+A where A is real number. We especially investigate the stability of equilibrium points, convergence of equilibrium points, existence of periodic solutions, and existence of bounded solutions of related system. Moreover, we present some numerical examples to verify the theoretical results.

scholarly journals BOUNDED SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS

1990 ◽  
Vol 21 (2) ◽  
pp. 137-142
Author(s):  
SUI-SUN CHENG ◽  
HORNG-JAAN LI
Keyword(s):  
Difference Equations ◽  
Bounded Solutions ◽  
Nonlinear Difference Equations

Bounded solutions of nonlinear difference equations.

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