 
Summary: Longtime stability estimates for the nonperiodic
Littlewood boundedness problem
Markus Kunze1
& Rafael Ortega2
1
Universit¨at DuisburgEssen, Fakult¨at f¨ur Mathematik,
D  45117 Essen, Germany
2
Departamento de Matem´atica Aplicada, Universidad de Granada,
E18071 Granada, Spain
Key words: Littlewood boundedness problem, bounded and unbounded
solutions, nonperiodic forcing, generating function
Abstract
We consider the nonlinear oscillator equation ¨x + x1x = p(t) for 3 and nonperiodic
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.
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