Asymptotic behavior of solutions to the perturbed simple pendulum problems with two parameters | Zendy

Shibata Tetsutaro | Zendy

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Asymptotic behavior of solutions to the perturbed simple pendulum problems with two parameters

Author(s) -

Shibata Tetsutaro

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410494

Subject(s) - mathematics , simple (philosophy) , eigenvalues and eigenvectors , constant (computer programming) , pendulum , mathematical analysis , mathematical physics , set (abstract data type) , pure mathematics , combinatorics , physics , quantum mechanics , computer science , programming language , philosophy , epistemology

We consider the perturbed simple pendulum equation– u ″( t ) + μ | u ( t )| p –1 u ( t ) = λ sin u ( t ), t ∈ I ≔ (– T , T ),u ( t ) > 0, t ∈ I ,u (± T ) = 0,where p > 1 is a constant, λ > 0 and μ ∈ R are parameters. The purpose of this paper is to clarify the structure of the solution set. To do this, we study precisely the asymptotic shape of the solutions when λ ≫ 1 as well as the asymptotic behavior of variational eigenvalue μ ( λ ) as λ → ∞. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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