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: [email protected] (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
SN - 0022-247X
VL - 304
SP - 511
EP - 530
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -