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)
Periodic solutions of a singular equation with indefinite weight. (English) Zbl 1232.34064

The authors study the existence and uniqueness of T-periodic solutions for the equation

x '' =a(t) x 3 ,

where a is a T-periodic function given by

a(t)=a + if0t<t + ,a(t)=-a - ift + t<T

with a + ,a - >0· These problems arise in different physical situations such as in the stabilization of matter-wave breathers in Bose-Einstein condensates, in the propagation of guided waves in optical fibers and in the electromagnetic trapping of a neutral atom near a charged wire. If the parameters a + ,a - are fixed, and T:=t + +t - , an interesting question is how to control the switching times t - ,t + in order to get periodic states with a particular amplitude. This question is studied in the paper as well as the stability properties (in the linear sense) of the T-periodic solutions.

MSC:
34C25Periodic solutions of ODE
34D20Stability of ODE