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

• 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

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.