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On necessary and sufficient conditions for numerical verification of double turning points

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Publication:1889957
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DOI10.1007/s00211-003-0515-4zbMath1058.65061OpenAlexW1969169294MaRDI QIDQ1889957

Sunao Murashige, Ken'ichiro Tanaka, Shin'ichi Oishi

Publication date: 13 December 2004

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-003-0515-4


zbMATH Keywords

nonlinear systemturning pointextended systemsnumerical veification


Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Algorithms with automatic result verification (65G20)


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Rigorous verification of saddle-node bifurcations in ODEs ⋮ Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation ⋮ Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity and their applications ⋮ Rigorous verification of Hopf bifurcations in functional differential equations of mixed type ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation



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