Ordinary differential equations on closed subsets of Fréchet spaces with applications to fixed point theorems

Polewczak, Jacek

doi:10.1090/S0002-9939-1989-1019755-6

Ordinary differential equations on closed subsets of Fréchet spaces with applications to fixed point theorems
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Proc. Amer. Math. Soc. 107 (1989), 1005-1012 Request permission

Abstract:

The construction and convergence of an approximate solution to the initial value problem $x’ = f(t,x),x(0) = {x_0}$, defined on closed subsets of a Fréchet space is given. Sufficient conditions that guarantee the existence of an approximate solution are analyzed in a relation to the Nagumo boundary condition used in the Banach space case. It is indicated that the Nagumo boundary condition does not guarantee the existence of an approximate solution. Applications to fixed points are given.

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Closed graph theorems and webbed spaces

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