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)
Nonlinear impulsive evolution equations. (English) Zbl 0932.34067

Summary: The author studies existence and uniqueness of mild and classical solutions to nonlinear impulsive evolution equations

u ' (t)=Au(t)+f(t,u(t)),0<t<T 0 ,tt i ,u(0)=u 0 ,
Δu(t i )=I i (u(t i )),i=1,2,,0<t 1 <t 2 <<T 0 ,

in a Banach space X, where A is the generator of a strongly continuous semigroup, Δu(t i )=u(t i + )-u(t i - ) and I i ’s are some operators. The impulsive conditions can be used to model more physical phenomena than the traditional initial value problems u(0)=u 0 . The author applies the semigroup theory to study existence and uniqueness of the mild solutions, and to show that the mild solutions give rise to classical solutions if f is continuously differentiable.

34G20Nonlinear ODE in abstract spaces
34A37Differential equations with impulses