Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial
碩士 === 國立臺南大學 === 應用數學系碩士班 === 102 === We study the exact multiplicity and the bifurcation curves of positive solutions of the boundary value problem u′′+λ(-u(u-β₁)(u-β₂)(u-β₃))=0,-1<x<1, u(-1)=u(1)=0, where λ>0 is a bifurcation parameter and the quartic polynomial nonlinearity f(u)=-u(u-...
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ndltd-TW-101NTNT05070012016-03-14T04:13:53Z http://ndltd.ncl.edu.tw/handle/63877550029930248491 Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial 包含四次多項式邊界值問題正解的分支曲線 Yi-Jung Lee 李貤溶 碩士 國立臺南大學 應用數學系碩士班 102 We study the exact multiplicity and the bifurcation curves of positive solutions of the boundary value problem u′′+λ(-u(u-β₁)(u-β₂)(u-β₃))=0,-1<x<1, u(-1)=u(1)=0, where λ>0 is a bifurcation parameter and the quartic polynomial nonlinearity f(u)=-u(u-β₁)(u-β₂)(u-β₃) has three positive zeros, 0<β₁≤β₂≤β₃. Then on the (λ,||u||∞)-plane, we obtain two qualitatively different bifurcation curves: a broken S-shaped curve, and a monotone increasing curve. Tzung-Shin Yeh 葉宗鑫 2014 學位論文 ; thesis 20 en_US |
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碩士 === 國立臺南大學 === 應用數學系碩士班 === 102 === We study the exact multiplicity and the bifurcation curves of positive solutions of the boundary value problem
u′′+λ(-u(u-β₁)(u-β₂)(u-β₃))=0,-1<x<1,
u(-1)=u(1)=0,
where λ>0 is a bifurcation parameter and the quartic polynomial nonlinearity f(u)=-u(u-β₁)(u-β₂)(u-β₃) has three positive zeros, 0<β₁≤β₂≤β₃. Then on the (λ,||u||∞)-plane, we obtain two qualitatively different bifurcation curves: a broken S-shaped curve, and a monotone increasing curve.
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Tzung-Shin Yeh |
author_facet |
Tzung-Shin Yeh Yi-Jung Lee 李貤溶 |
author |
Yi-Jung Lee 李貤溶 |
spellingShingle |
Yi-Jung Lee 李貤溶 Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
author_sort |
Yi-Jung Lee |
title |
Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
title_short |
Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
title_full |
Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
title_fullStr |
Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
title_full_unstemmed |
Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial |
title_sort |
bifurcation curves of positive solutions for a boundary value problem with a quartic polynomial |
publishDate |
2014 |
url |
http://ndltd.ncl.edu.tw/handle/63877550029930248491 |
work_keys_str_mv |
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