Interior transition layers of solutions to the perturbed elliptic Sine-Gordon equation on an interval |
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Authors: | Tetsutaro Shibata |
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Affiliation: | (1) The Division of Mathematical and Information Sciences Faculty of Integrated Arts and Sciences, Hiroshima University, 739-8521 Higashi-Hiroshima, Japan |
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Abstract: | We consider the perturbed elliptic Sine-Gordon equation on an interval-u″t+γsinu(t)=μf(u(t)),t ∈I := (-T, T),u(t) > 0,t ∈I,u(±T)=0 where λ, μ>0 are parameters andT>0 is a constant. By applying variational methods subject to the constraint depending on λ, we obtain eigenpairs (μ,u)=(μ(λ),u λ) which solve this eigenvalue problem for a given λ>0. Then we study the asymptotic behavior ofu λ and μ(λ) as λ→∞. Especially, we study the location of interior transition layers ofu λ as λ→∞. This research has been supported by the Japan Society for the Promotion of Science. |
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