Layer structures for the solutions to the perturbed simple pendulum problems

DOI10.1016/j.jmaa.2005.06.049zbMath1102.34015OpenAlexW1984450404MaRDI QIDQ819681

Tetsutaro Shibata

Publication date: 29 March 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://ir.lib.hiroshima-u.ac.jp/files/public/1/15347/20141016123102909635/93newrevised2.pdf

zbMATH Keywords

singular perturbationminimization problemboundary layerinterior layersimple pendulum problem

Mathematics Subject Classification ID

Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Singular perturbations for ordinary differential equations (34E15)

Cites Work

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• Asymptotics of eigencurves for second order ordinary differential equations. I
• Phase-plane solutions to some singular perturbation problems
• The principal eigencurve for the \(p\)-Laplacian
• Bifurcation from eigencurves of the \(p\)-Laplacian
• Multiple interior layers of solutions to perturbed elliptic Sine-Gordon equation on an interval
• Precise spectral asymptotics for the Dirichlet problem \(-u(t)+g(u(t))=\lambda\sin u(t)\)
• Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems
• Uniform convergence of multiparameter eigenfunction expansions
• Bifurcation from eigenvalues in nonlinear multiparameter problems
• Asymptotic behavior of eigenvalues for two-parameter perturbed elliptic sine-Gordon type equations
• Interior transition layers of solutions to the perturbed elliptic sine-Gordon equation on an interval

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