Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

A class of nonlinear delay evolution equations with nonlocal initial conditions


Authors: Monica-Dana Burlică and Daniela Roşu
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
Published electronically: March 28, 2014
MathSciNet review: 3195766
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 34K05, 34K13, 34K20, 34K30, 35K55, 35K65, 47H05

Retrieve articles in all journals with MSC (2010): 34K05, 34K13, 34K20, 34K30, 35K55, 35K65, 47H05


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

Keywords: Differential delay evolution equation, nonlocal delay initial condition, periodic solutions, metric fixed point arguments, nonresonance condition, nonlinear parabolic equations.
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.