zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Existence for a class of partial functional differential equations with infinite delay. (English) Zbl 1003.34068

The authors study the following class of functional-differential equations with infinite delay in a Banach space E

x ' (t)=Ax(t)+F(t,x t ),t0,x 0 =ϕ,

where A is a closed linear operator. Existence, uniqueness and regularity results for the same class of equations were previously furnished by H. R. Henríquez [Funkc. Ekvacioj, Ser. Int. 37, No. 2, 329–343 (1994; Zbl 0814.35141); Indian J. Pure Appl. Math. 27, No. 4, 357–386 (1996; Zbl 0853.34072) and Nonlinear Anal., Theory Methods Appl. 28, No. 3, 513–531 (1997; Zbl 0864.35112)] in the case where A is an infinitesimal generator of a C 0 -semigroup on E.

The aim of the present paper is to extend such existence results to the case where A is a Hille-Yosida operator with domain D(A) not necessarily dense in E. The theory of integrated semigroups is the main tool used. The authors apply the result to a partial integrodifferential equation.

MSC:
34K30Functional-differential equations in abstract spaces
35R10Partial functional-differential equations
35R20Partial operator-differential equations
47D62Integrated semigroups