## 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
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## 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 $\alpha (t)$.

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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