ABSTRACT
For a linear equation Lx — f the notion of “D-stability” (“D-property”) is in troduced as a correct solvability of the Cauchy problem Lx = / , x(a) = a in a prescribed functional Banach space D , depending on the right-hand side of / from the prescribed functional Banach space B and the initial value a from a finite di mensional space R n. Under the appropriate choice of spaces B and D the presence of D-property ensures this or that kind of stability in a classical sense. The choice of the space D proposed in Chapter 2 appears to be optimal in the sense that every element x £ D is a solution to the equation Lx = / for corresponding / G f i , and a £ R n. This allows us to avoid extra arguments not related to the essence of the problem and permits short and explicit formulations and proofs of the assertions on the presence of the required properties of the discussed equation. In particular, D-stability is ensured by the invertibility of linear operator written in the explicit form.
