## A class of nonlinear delay evolution equations with nonlocal initial conditions

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- by Monica-Dana Burlică and Daniela Roşu PDF
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**142**(2014), 2445-2458 Request permission

## Abstract:

We establish a sufficient condition for the existence, uniqueness and global uniform asymptotic stability of a $C^0$-solution for the nonlinear delay differential evolution equation \begin{equation*}\left \{\begin {array}{ll} \displaystyle u’(t)\in Au(t)+f(t,u_t),&\quad t\in \mathbb {R}_+, \\[1mm] u(t)=g(u)(t),&\quad t\in [ -\tau ,0 ], \end{array}\right .\end{equation*} where $\tau >0$, $X$ is a real Banach space, $A$ is the infinitesimal generator of a nonlinear semigroup of contractions, $f:\mathbb {R}_+\times C([ -\tau ,0 ];\overline {D(A)})\to X$ is continuous and $g:C_b([ -\tau ,+\infty );\overline {D(A)})\to C([ -\tau ,0 ];\overline {D(A)})$ is nonexpansive.## References

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## Additional Information

**Monica-Dana Burlică**- Affiliation: Department of Mathematics and Informatics, “G. Asachi” Technical University, Bvd. Carol I, no. 11 A, Iaşi, 700506, Romania
- Email: monicaburlica@yahoo.com
**Daniela Roşu**- Affiliation: Department of Mathematics and Informatics, “G. Asachi” Technical University, Bvd. Carol I, no. 11 A, Iaşi, 700506, Romania
- Email: rosudaniela100@yahoo.com
- Received by editor(s): June 14, 2012
- Received by editor(s) in revised form: July 30, 2012
- Published electronically: March 28, 2014
- Additional Notes: This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS–UEFISCDI, project number PN-II-ID-PCE-2011-3-0052.
- Communicated by: Yingfei Yi
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**142**(2014), 2445-2458 - MSC (2010): Primary 34K05, 34K13, 34K20, 34K30, 35K55, 35K65, 47H05
- DOI: https://doi.org/10.1090/S0002-9939-2014-11969-1
- MathSciNet review: 3195766