zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Solvability of the Cauchy problem for infinite delay equations. (English) Zbl 1058.34106

By using topological methods, expressed in terms of the Kuratowski measure of noncompactness, the authors prove several existence results on mild solutions for the infinite delay functional-integral equation

u(t)=g(t)+ σ t f(t,s,u(s),u s )ds,σtT,u σ =ϕ,

and semilinear functional-differential equations of the form

u ' (t)=Au(t)+f(t,u(t),u t ),0tT,u 0 =ϕ,

with ϕ. Here, is an admissible function space, i.e., a suitable chosen subspace of functions from (-,σ] to X, with X a Banach space, ϕ, x t (s)=x(t+s), f is either in C([σ,T]×[σ,T]×X×;X) or in C([σ,T]×X×;X) and A:D(A)XX is a linear operator. An extension to the case when A may depend on t as well is considered, and an application to a functional integro-differential equation of Schrödinger type is included.

34K30Functional-differential equations in abstract spaces
47D62Integrated semigroups
35Q55NLS-like (nonlinear Schrödinger) equations
35K05Heat equation