An introduction to difference equations
An introduction to difference equations
| Hi-index | 0.98 |
We suppose that M is a closed subspace of l^~(J, X), the space of all bounded sequences {x(n)}"n"@?"J @? X, where J @? {Z^+, Z} and X is a complex Banach space. Consider the operator difference equation , where @j @? l^~(Z, X) such that the restriction @j|"J on J belongs to M, and A is the generator of a C"0-semigroup of linear bounded operators (T(t))"t"="0 on X. Certain conditions will be imposed to guarantee the existence of solutions in the class M. We deduce that the zero equilibrium of the homogeneous equation , is globally asymptotically stable iff every solution is bounded.