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 to boundary value problems for impulsive second order differential inclusions. (English) Zbl 0784.34012
The authors consider a second order differential inclusion $y''\in F(t,y,y')$ subject to a set of nonlinear boundary constraints $$y(t\sb k\sp +)= l\sb k(y(t\sb k)) \qquad y'(t\sb k\sp +)= N\sb k(y(t\sb k),y'(t\sb k))$$ where $l\sb k$ are given homeomorphisms and $N\sb k$ are continuous, moreover $$G\sb i(y(a\sb 0),y'(a\sb 0), y(a\sb 1),y'(a\sb 1)), \quad i=1,2$$ where $a\sb 0=t\sb 0<t\sb 1<\cdots <t\sb m<t\sb{m+1}=a\sb 1$. Their main existence result, Theorem 2.2, is proved by means of the topological transversality method of Granas based on the existence of a priori bounds for the solutions of the above boundary value problem which is suitably modified to deal with the impulsive nature of the problem. Two motivating examples involving impulses are presented.

34A60Differential inclusions
34A37Differential equations with impulses
34B15Nonlinear boundary value problems for ODE
Full Text: DOI