TY - JOUR

T1 - On exponential dichotomy, Bohl-Perron type theorems and stability of difference equations

AU - Berezansky, L.

AU - Braverman, Elena

N1 - Funding Information:
* Corresponding author. E-mail address: maelena@math.ucalgary.ca (E. Braverman). 1 Partially supported by Israeli Ministry of Absorption. 2 Partially supported by the NSERC Research Grant and the AIF Research Grant.

PY - 2005/4/15

Y1 - 2005/4/15

N2 - For a delay difference equation x(n + 1) = ∑k=-dn A(n, k)x(k) + f(n) in a Banach space the following result is proved: if for any f ∈ lp the solution is x ∈ lp then the solution of the homogeneous equation (f ≡ 0) is exponentially stable. This result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation.

AB - For a delay difference equation x(n + 1) = ∑k=-dn A(n, k)x(k) + f(n) in a Banach space the following result is proved: if for any f ∈ lp the solution is x ∈ lp then the solution of the homogeneous equation (f ≡ 0) is exponentially stable. This result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation.

KW - Difference equations

KW - Explicit stability conditions

KW - Exponential dichotomy

KW - Exponential stability

UR - http://www.scopus.com/inward/record.url?scp=14844290879&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2004.09.042

DO - 10.1016/j.jmaa.2004.09.042

M3 - Article

AN - SCOPUS:14844290879

VL - 304

SP - 511

EP - 530

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -