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)
Almost periodic solutions of neutral functional differential equations. (English) Zbl 1142.34367
Summary: We study a non-autonomous neutral functional differential equation in a Banach space. Applying the theory of semigroups of operators to evolution equations and Krasnoselskii’s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration.

34K14Almost and pseudo-periodic solutions of functional differential equations
34K40Neutral functional-differential equations
Full Text: DOI
[1] B.M. Levitan, V. Zhikov, Almost Periodic Functions and Differential Equations, Moscow, 1978 · Zbl 0414.43008
[2] Besicovich, A. S.: Almost periodic functions, (1958)
[3] Amerio, L.; Prouse, G.: Almost periodic functions and functional equations, (1971) · Zbl 0215.15701
[4] Rubanik, V. P.: Oscillations of quasilinear systems with retardation, (1969)
[5] Hale, J. K.; Lunel, V. M.: Introduction to functional differential equations, Appl. math. Sci. 99 (1993) · Zbl 0787.34002
[6] Gurtin, M. E.; Pipkin, A. C.: A general theory of heat conduction with finite wave speed, Arch. ration. Mech. anal. 31, 113-126 (1968) · Zbl 0164.12901 · doi:10.1007/BF00281373
[7] Zaidman, S.: Abstract differential equations, (1979) · Zbl 0465.34002
[8] Zaidman, S.: Topics in abstract differential equations 1, Pitman research notes in mathematics 304 (1994) · Zbl 0806.34001
[9] Zaidman, S.: Topics in abstract differential equations 2, Pitman research notes in mathematics 321 (1995) · Zbl 0834.34001
[10] Islam, Mohammad N.; Raffoul, Youssef N.: Periodic solutions of neutral nonlinear system of differential equations with functional delay, J. math. Anal. appl. 331, 1175-1186 (2007) · Zbl 1118.34057 · doi:10.1016/j.jmaa.2006.09.030
[11] Acquistapace, P.; Terreni, B.: A unified approach to abstract linear parabolic equations, Rend. sem. Math. uni. Padova 78, 47-107 (1987) · Zbl 0646.34006 · numdam:RSMUP_1987__78__47_0
[12] Acquistapace, P.: Evolution operators and strong solution of abstract linear parabolic equations, Differential integral equations 1, 433-457 (1988) · Zbl 0723.34046