Nonlinear evolution equations and product integration in Banach spaces.

Webb, G. F.

doi:10.1090/S0002-9947-1970-0265992-8

Nonlinear evolution equations and product integration in Banach spaces.
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Trans. Amer. Math. Soc. 148 (1970), 273-282 Request permission

Abstract:

The method of product integration is used to obtain solutions to the nonlinear evolution equation $g’ = Ag$ where A is a function from a Banach space S to itself and g is a continuously differentiable function from $[0,\infty )$ to S. The conditions required on A are that A is dissipative on S, the range of $(e - \varepsilon A) = S$ for all $\varepsilon \geqq 0$, and A is continuous on S.

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