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

DOI:
https://doi.org/10.1090/S0002-9939-1989-1019755-6

MathSciNet review:
1019755

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Abstract: The construction and convergence of an approximate solution to the initial value problem , 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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Additional Information

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