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On two noteworthy deformations of negatively curved Riemannian metrics
Pazytype characterization for differentiability of propagators of higher order Cauchy problems in Banach spaces
1.  Department of Mathematics, University of Science and Technology of China, Hefei 230026, China, China 
$u^{(n)}(t) +\sum_{k=0}^{n1}A_ku^{(k)}(t)=0, t\geq 0,$
$u^{(k)}(0) = u_k, 0\leq k\leq n1,
where $A_0, A_1,\ldots, A_{n1}$ are densely defined closed linear operators on a Banach space. A Pazytype characterization of the infinitely differentiable propagators of the Cauchy problem is obtained. Moreover, two related sufficient conditions are given.
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