Simple proof of stationary phase method and application to oscillatory bifurcation problems

Simple proof of stationary phase method and application to oscillatory bifurcation problems

We consider the nonlinear eigenvalue problem −u′′(t)=λf(u(t)),u(t)>0,t∈I≔(−1,1),u(±1)=0, where f(u)=f1(u)=u3+sin(u3)∕u, f(u)=f2(u)=u+upsin(uq) (0≤p

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Veröffentlicht in:Nonlinear analysis 2020-01, Vol.190, p.111594, Article 111594
Hauptverfasser: Kato, Keiichi, Shibata, Tetsutaro
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Sprache:eng
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Asymptotic methods
Bifurcations
Eigenvalues
Global structure
Nonlinear eigenvalue problems
Oscillatory bifurcation
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description We consider the nonlinear eigenvalue problem −u′′(t)=λf(u(t)),u(t)>0,t∈I≔(−1,1),u(±1)=0, where f(u)=f1(u)=u3+sin(u3)∕u, f(u)=f2(u)=u+upsin(uq) (0≤p
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subjects Asymptotic methods
Bifurcations
Eigenvalues
Global structure
Nonlinear eigenvalue problems
Oscillatory bifurcation
title Simple proof of stationary phase method and application to oscillatory bifurcation problems
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