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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Main Authors: Yi-Jung Lee, 李貤溶
Other Authors: Tzung-Shin Yeh
Format: Others
Language:en_US
Published: 2014
Online Access:http://ndltd.ncl.edu.tw/handle/63877550029930248491
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spelling 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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language en_US
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description 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.
author2 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
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