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)
Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α-norm. (English) Zbl 1185.34112

The authors consider the existence of solutions of the neutral partial differential equation with nonlocal conditions:

d/dtx ( t ) + F ( t , x ( t ) )=-Ax(t)+G(t,x(t)),t0,
x(0)+g(x)=x 0 X,

where -A generates an analytic compact semigroup on a Banach space X and where the functions F, G and g satisfy specific continuity and measurability constraints. Fractional powers of -A are used. By the fixed point theorem of Sadovskii existence of a mild solution is obtained. When X is a reflexive Banach space and G is Lipschitz continuous, a strong solution is obtained. The results are applied to a class of partial differential equations with nonlocal conditions.

34K30Functional-differential equations in abstract spaces
34K40Neutral functional-differential equations
35R10Partial functional-differential equations
47D06One-parameter semigroups and linear evolution equations