zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 for a class of second-order Hamiltonian systems with impulsive effects. (English) Zbl 1193.34057

The authors give sufficient conditions the existence of a solution to the following boundary value problem

u ¨(t)=F(t,u(t))a.e.t[0,T];u(0)-u(T)=u ˙(0)-u ˙(T)=0,u ˙ j (t j )=u ˙ j (t j + )-u ˙ j (t j - )=I ij (u i (t j )),i=1,2,,N;j=1,2,,p·

Here, t 0 =0<t 1 <t 2 <<t p <t p+1 =T,u(t)=(u 1 (t),u 2 (t),,u N (t)),I ij : (i=1,2,,N, j=1,2,,p) are continuous and F:[0,T]× N satisfies the following assumption:

(A) F(t,x) is measurable in t for every x N and continuously differentiable in x for a.e. t[0,T] and there exist aC( + , + ),bL 1 (0,T; + ) such that

|F(t,x)|a(|x|)b(x),|F(t,x)|a(|x|)b(x)

for all x N and a.e. t[0,T].

Two illustrative examples are given.

MSC:
34B37Boundary value problems for ODE with impulses
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems