Set-Valued and Variational Analysis

, Volume 20, Issue 3, pp 477–497

Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions

Article

DOI: 10.1007/s11228-012-0203-6

Cite this article as:
Vrabie, I.I. Set-Valued Var. Anal (2012) 20: 477. doi:10.1007/s11228-012-0203-6

Abstract

We prove a sufficient condition for the existence of global C0-solutions for a class of nonlinear functional differential evolution equation of the form
$$ \left\{\begin{array}{ll} \displaystyle u'(t)\in Au(t)+f(t),&t\in\mathbb{R}_+, \\[2mm] f(t)\in F(t,u(t),u_t),&t\in\mathbb{R}_+, \\[2mm] u(t)=g(u)(t),& t\in [\,-\tau,0\,], \end{array}\right. $$
where X is a real Banach space, A generates a nonlinear compact semigroup having an exponential decay, \(F:\mathbb{R}_+\times X\times C([\,-\tau,0\,];\overline{D(A)})\rightsquigarrow X\) is a nonempty, convex, weakly compact valued and almost strongly-weakly u.s.c. multi-function with linear growth and the nonlocal function \(g:C_{b}([\,-\tau,+\infty);\overline{D(A)})\to C([\,-\tau,0\,];\overline{D(A)})\) is nonexpansive.

Keywords

Functional differential evolution equation Delay evolution inclusion Nonlocal initial condition Multi-function Compact semigroup 

Mathematics Subject Classifications (2010)

34K30 34G25 34K99 47H06 47J35 34K05 

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics“Al. I. Cuza University”IaşiRomania
  2. 2.“O. Mayer” Institute of Mathematics, Romanian AcademyIaşiRomania

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