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)
Basic results for functional differential and dynamic equations involving impulses. (English) Zbl 1266.34115
Measure functional differential equations of the form $$x(t)=x(t_0)+\int_{t_{0}}^tf(x_s,s)dg(s),\quad t\in [t_0,t_0+\sigma],\quad x(t_0)=\phi$$ and impulsive measure functional differential equations of the form $$x(t)=x(t_0)+\int_{t_{0}}^tf(x_s,s)dg(s)+\sum_{k\in\{1,\dotsc,m\}, t_{k}<t}I_k(x(t_{k})), \quad t\in [t_0,t_0+\sigma],\quad x(t_0)=\phi$$ are studied, where the integrals on the right-hand side are the Kurzweil-Henstock-Stieltjes integrals with respect to a nondecreasing function $g$. The relation between measure functional differential equations, impulsive measure functional differential equations and impulsive functional dynamic equations on time scales is described. Existence and uniqueness of solutions, continuous dependence and periodic averaging for both types of impulsive measure functional differential equations are presented. The paper is a continuation of the author’s paper [J. Differ. Equations 252, No. 6, 3816--3847 (2012; Zbl 1239.34076)].

34K05General theory of functional-differential equations
34K45Functional-differential equations with impulses
34N05Dynamic equations on time scales or measure chains
34K33Averaging (functional-differential equations)
Full Text: DOI