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Proceedings of the American Mathematical Society

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


Author: Jacek Polewczak
Journal: Proc. Amer. Math. Soc. 107 (1989), 1005-1012
MSC: Primary 47H15; Secondary 34A05, 34G20, 47H10
MathSciNet review: 1019755
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-1019755-6
Keywords: Fréchet space, approximate solution to initial value problem, solution of IVP, fixed point theory
Article copyright: © Copyright 1989 American Mathematical Society