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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Asymptotic behavior of solutions of nonlinear functional differential equations in Banach space
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by John R. Haddock
Trans. Amer. Math. Soc. 231 (1977), 83-92
DOI: https://doi.org/10.1090/S0002-9947-1977-0442404-9

Abstract:

Let X be a Banach space and let $C = C([ - r,0],X)$ denote the space of continuous functions from $[ - r,0]$ to X. In this paper the problem of convergence in norm of solutions of the nonlinear functional differential equation $\dot x = F(t,{x_t})$ is considered where $F:[0,\infty ) \times C \to X$. As a special case of the main theorem, stability results are given for the equation $\dot x(t) = f(t,x(t)) + g(t,{x_t})$, where $- f(t, \cdot ) - \alpha (t)I$ satisfies certain accretive type conditions and $g(t, \cdot )$ is Lipschitzian with Lipschitz constant $\beta (t)$ closely related to $\alpha (t)$.
References
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 231 (1977), 83-92
  • MSC: Primary 34G05; Secondary 34K20
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0442404-9
  • MathSciNet review: 0442404