TY - JOUR

T1 - New stability conditions for linear difference equations using Bohl-Perron type theorems

AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information:
The authors are grateful to the referee for valuable comments and remarks. L. Berezansky was partially supported by the Israeli Ministry of Absorption and E. Braverman was partially supported by the NSERC Research Grant.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

AB - The Bohl-Perron result on exponential dichotomy for a linear difference equation states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function.

KW - Exponential stability

KW - Linear delay difference equations

KW - Positive fundamental function

UR - http://www.scopus.com/inward/record.url?scp=79957469938&partnerID=8YFLogxK

U2 - 10.1080/10236190903146938

DO - 10.1080/10236190903146938

M3 - Article

AN - SCOPUS:79957469938

SN - 1023-6198

VL - 17

SP - 657

EP - 675

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

IS - 5

ER -