BOUNDEDNESS FOR SEMILINEAR DUFFING EQUATIONS AT RESONANCE

In this paper, we prove the boundedness of all solutions for the equationxʺ +n 2 x+ϕ(x) +gʺ(x)q(t) = 0, wheren∈ ℕ,q(t) =q(t+ 2π),ϕ(x) andg(x) are bounded. 2010Mathematics Subject Classification: 35A24, 70H08. Key words and phrases: Hamiltonian system, Boundedness of solutions, Canonical transformati...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 5; pp. 1923 - 1949
Main Authors Xing, Xiumei, Wang, Yiqian
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2012
Subjects
Lagrangian function
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Summary:In this paper, we prove the boundedness of all solutions for the equationxʺ +n 2 x+ϕ(x) +gʺ(x)q(t) = 0, wheren∈ ℕ,q(t) =q(t+ 2π),ϕ(x) andg(x) are bounded. 2010Mathematics Subject Classification: 35A24, 70H08. Key words and phrases: Hamiltonian system, Boundedness of solutions, Canonical transformation, Moser's small twist theorem.
ISSN:1027-5487
2224-6851