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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A class of nonlinear delay evolution equations with nonlocal initial conditions
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by Monica-Dana Burlică and Daniela Roşu PDF
Proc. Amer. Math. Soc. 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.
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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