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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Differential equations on closed subsets of a Banach space


Authors: V. Lakshmikantham, A. Richard Mitchell and Roger W. Mitchell
Journal: Trans. Amer. Math. Soc. 220 (1976), 103-113
MSC: Primary 34G05
MathSciNet review: 0402224
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Abstract: The problem of existence of solutions to the initial value problem $ x' = f(t,x),x({t_0}) = {x_0} \in F$, where $ f \in C[[{t_0},{t_0} + a] \times F,E]$, F is a locally closed subset of a Banach space E is considered. Nonlinear comparison functions and dissipative type conditions in terms of Lyapunov-like functions are employed. A new comparison theorem is established which helps in surmounting the difficulties that arise in this general setup.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0402224-7
Keywords: Banach space, nonlinear differential equation, dissipative type conditions
Article copyright: © Copyright 1976 American Mathematical Society