On Noetherian index of differential/algebraic systems. I
Under consideration is the problem \(\Lambda x : = A(t) \dot x + B(t)x = f\), \(t \in T = [\alpha, \beta]\), \(x(\alpha) = a\), where \(A(t)\) and \(B(t)\) and \((n \times n)\)-matrics whose smoothness will be specified in formulations, \(f \equiv f(t)\) and \(x \equiv x(t)\) are known and unknown \(n\)-dimensional vector-functions, and the dot denotes differentiation with respect to \(t\). We suppose that \(\text{det} A(t) = 0\) \(\forall t \in T\). In the present article we study properties of the operators \(\Lambda : E \to F\) and \(\Lambda_ a : E \to F \times \mathbb{R}^ n\), where \(\Lambda_ ax = \{\Lambda x; x(\alpha)\}\), \(E\) and \(F\) are topological vector or Banach spaces, and in the first case \(E=F=C^ \infty(T)\), and in the second case \(E=C^ 1(T)\) and \(F=\Lambda C^ 1(T)\).
scientific article; zbMATH DE number 641323