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)
Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces. (English) Zbl 0889.45016
The paper deals with a periodic boundary value problem for a second order nonlinear integro-differential equation with impulses at fixed moments in a Banach space. The concepts of lower and upper solutions for this problem are introduced and then the monotone iterative method is used to construct a couple of monotone sequences converging to the extremal solutions of the problem in a sector defined by a lower solution $u_{0}$ and an upper solution $v_{0}$, with $u_{0}\leq v_{0}$. For it, the authors first study a periodic boundary value problem for a linear impulsive integro-differential equation and prove a comparison result.

45N05Abstract integral equations, integral equations in abstract spaces
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045
[2] Guo, D.; Liu, X.: Extremal solutions of nonlinear impulsive integro-differential equations in Banach spaces. J. math. Anal. appl. 177, 538-552 (1993) · Zbl 0787.45008
[3] Du, Y.: Fixed points of increasing operators in ordered Banach spaces and applications. Appl. anal. 38, 1-20 (1990) · Zbl 0671.47054
[4] Liu, X.: Monotone iterative technique for impulsive differential equations in a Banach space. J. math. Phy. sci. 24, 183-191 (1990) · Zbl 0717.34068
[5] Liu, X.; Guo, D.: Initial value problems for first order impulsive integro-differential equations in Banach spaces. Comm. appl. Nonl. anal. 2, 65-83 (1995) · Zbl 0858.34068