Abstract
The main result gives conditions under which the Riccati equation $S'(t) = A(t)S(t) + S(t)B(t) + S(t)C(t)S(t) + D(t)$ with initial condition $S(0) = S_0 $ has a strongly differentiable solution. In addition, equations of more general form, but with more restrictive initial conditions, are shown to have solutions which are differentiable with respect to the uniform topology. These results, as well as their proofs, are discussed in the context of an important problem in transport theory.
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