-boundedness properties for Volterra difference equations

Cuevas, Claudio; Dantas, Filipe; Choquehuanca, Mario; Soto, Herme

doi:10.1016/j.amc.2012.12.053

Cited by 8 publications

(12 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The following result provides conditions for the existence of solutions of . Such result generalize Cuevas et al, Theorem 1.3…”

Section: Introduction and Statement Of The Main Resultssupporting

confidence: 87%

“…For example, Castro et al investigate the existence of discrete almost automorphic solutions, and also, the authors have studied the asymptotic behavior of the solutions. Cuevas et al deal with l p ‐boundedness properties for equations of type . The effect of different kinds of the nonhomogeneous term were taken into consideration consequently they loss uniqueness of solutions.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…The effect of different kinds of the nonhomogeneous term were taken into consideration consequently they loss uniqueness of solutions. Cuevas et al deal with the asymptotic behavior, the continuity, and the compactness properties of solutions for equations of type .…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…Example Let α , β , c , and d be real numbers so that | α | < 1 and

false(false| c false| + 2 false| d false| false) < \frac{1 - false| α false|}{{false| false| u false| false|}_{ℓ^{\infty} false(double-struckZ; double-struckR false)}}

, where u ( n ) is a control input in

ℓ^{1} false(double-struckZ; double-struckR false)

. We consider the following discrete control systems which were considered in other studies():

x false(n + 1 false) = α x false(n false) + β u false(n false), n \in double-struckZ,

x false(n + 1 false) = α x false(n false) + β u false(n false) + c x false(n false) s i n u false(n false) + d u false(n false) c o s^{2} x false(n false), n \in double-struckZ .

Based on the state space quantization method used by Delchamps (see also Nair and Evans), Phat and Jiang established sufficient conditions for the global stabilizability of the semilinear system . In our framework, we consider the phase space

B^{γ} false(double-struckR false)

, γ > 0, in order to model the control system .…”

Section: Applications and Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Qualitative theory for Volterra difference equations

Bernardo

Cuevas

Soto

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The following result provides conditions for the existence of solutions of . Such result generalize Cuevas et al, Theorem 1.3…”

Section: Introduction and Statement Of The Main Resultssupporting

confidence: 87%

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…Example Let α , β , c , and d be real numbers so that | α | < 1 and

false(false| c false| + 2 false| d false| false) < \frac{1 - false| α false|}{{false| false| u false| false|}_{ℓ^{\infty} false(double-struckZ; double-struckR false)}}

, where u ( n ) is a control input in

ℓ^{1} false(double-struckZ; double-struckR false)

. We consider the following discrete control systems which were considered in other studies():

x false(n + 1 false) = α x false(n false) + β u false(n false), n \in double-struckZ,

x false(n + 1 false) = α x false(n false) + β u false(n false) + c x false(n false) s i n u false(n false) + d u false(n false) c o s^{2} x false(n false), n \in double-struckZ .

B^{γ} false(double-struckR false)

, γ > 0, in order to model the control system .…”

Section: Applications and Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Qualitative theory for Volterra difference equations

Bernardo

Cuevas

Soto

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Asymptotic analysis of difference equations of the form (5) or its explicit version often appeared in literature in the last decades. Some of them deal with the convolution case ( , = − ); see, for instance, [6] and the references therein and [7][8][9][10][11][12]. Most of the known results for the nonconvolution case are based on the hypothesis of double summability of the coefficients (∑ +∞ =0 ∑ =0 | , | < +∞); see [1,4,[13][14][15][16][17][18][19].…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 99%

Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations

Messina

Vecchio

2018

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

On exponential stability of nonlinear Volterra difference equations in phase spaces

Ngoc

Hieu

2014

Math. Nachr.

View full text Add to dashboard Cite

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18, 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.

show abstract

-boundedness properties for Volterra difference equations

Cited by 8 publications

References 21 publications

Qualitative theory for Volterra difference equations

Qualitative theory for Volterra difference equations

Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations

On exponential stability of nonlinear Volterra difference equations in phase spaces

Contact Info

Product

Resources

About