Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Long-time stability estimates for the non-periodic Littlewood boundedness problem

Summary: Long-time stability estimates for the non-periodic
Littlewood boundedness problem
Markus Kunze1
& Rafael Ortega2
Universit¨at Duisburg-Essen, Fakult¨at f¨ur Mathematik,
D - 45117 Essen, Germany
Departamento de Matem´atica Aplicada, Universidad de Granada,
E-18071 Granada, Spain
Key words: Littlewood boundedness problem, bounded and unbounded
solutions, non-periodic forcing, generating function
We consider the nonlinear oscillator equation ¨x + |x|-1x = p(t) for 3 and non-periodic
forcing p. For any solution x which is unbounded in the (x, x)-phase plane it is shown that,
for > 0 small enough, there is a solution x which is bounded in the phase plane and such
that the actions of x and x remain close on a time interval of length -2; further precise
information is available on the location of the zeros of x. In addition, it is possible to take
the bounded solution x from a fixed countable family of such solutions.


Source: Arias, Cristina M. - Departamento de Matemática Aplicada, Universidad de Granada


Collections: Mathematics