Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial

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Main Authors: , Others en_US 2014 http://ndltd.ncl.edu.tw/handle/63877550029930248491
id ndltd-TW-101NTNT0507001 oai_dc 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,-10 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 NDLTD en_US Others NDLTD 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,-10 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 Tzung-Shin Yeh Yi-Jung Lee 李貤溶 Yi-Jung Lee 李貤溶 Yi-Jung Lee 李貤溶 Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial Yi-Jung Lee Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial Bifurcation Curves of Positive Solutions for A Boundary Value Problem with A Quartic Polynomial bifurcation curves of positive solutions for a boundary value problem with a quartic polynomial 2014 http://ndltd.ncl.edu.tw/handle/63877550029930248491 AT yijunglee bifurcationcurvesofpositivesolutionsforaboundaryvalueproblemwithaquarticpolynomial AT lǐyíróng bifurcationcurvesofpositivesolutionsforaboundaryvalueproblemwithaquarticpolynomial AT yijunglee bāohánsìcìduōxiàngshìbiānjièzhíwèntízhèngjiědefēnzhīqūxiàn AT lǐyíróng bāohánsìcìduōxiàngshìbiānjièzhíwèntízhèngjiědefēnzhīqūxiàn 1718204192023117824