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Higher-order degenerate Cauchy problems in locally convex spaces. (English) Zbl 1096.34035
Using the so-called \(C\)-propagation family of operators, the authors give conditions for the \(C\)-well-posedness of the higher-order degenerate Cauchy problem \[ \frac{d^n}{dt^n}Bu(t) = Au(t), t \geq 0, \;(Bu)^{(k)}(0)=Bu_k, 0 \leq k \leq n-1, \tag{1} \] where \(A\) and \(B\) are closed linear operators in a sequentially complete locally convex topological space. As an application, problem (1) with \(n=2\) and differential operators \(A\) and \(B\) is considered.

MSC:
34G10 Linear differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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