Stability of neutral differential difference systems with infinite delays

✍ Scribed by Wanbiao Ma; Yasuhiro Takeuchi

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 1005 KB
• Volume: 33
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(97)00546-4

✦ Synopsis

It is well known that UCg is an admissible space and BC can be continuously embedded in UCg (see, for example, ). We use the same symbol I[" II to denote the norms in R" and BC, but no confusion will occur.

An n × n real constant matrix C = (cu)n× . with c o <_ 0 (i ~ j; i,j --1, 2 ..... n) is said to be an M-matrix, if and only if there is a vector v e R" such that v > 0 and Cv > 0 or CTv > 0 (see, for example, ). The nonlinear functions satisfying the following Definition 1.1 can be considered as a kind of generalization of an M-matrix in the sense that we consider mapping G(x) = Cx: R+ -~ R n for any M-matrix C. Definition 1.1. Let/~+ be an open subset of R+ with x = 0 ~ OD+.