Integrated Solutions to Implicit Differenti Al Equations
نویسنده
چکیده
This paper establishes in two completely different ways that the abstract degenerate initial value problem —(Mu(t)) + Lu{t) = f(t),Q < t < r ,Mu(0) = Uh Muo, has always an integrated solution, provided that for ali complex numbers z in the half-plane Rez > a > 0 the operator pencil P(z) = zM + L has a bounded inverse from the Banach space X to T>(L), endowed with the graph-norm, and its norm has a polynomial growth there. Some applications to partial differential equations are given. A Trotter-Kato type result is proved, too.
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