An Explicit Formula and Asymptotic Behaviors of Bifurcation Curve of a Boundary Blow-up Problem

• Main Authors: I-An Cho, 卓益安
• Other Authors: Shin-Hwa Wang
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/67144005151724175480

碩士 === 國立清華大學 === 數學系 === 89 === We consider the bifurcation curve of (sign-changing and nonnegative) solutions of the boundary blow-up problem where λ is a positive bifurcation parameter and f is locally Lipschitz continuous at all points in R except possibly at some point s where f(s)=0 and f is continuous there. In particular, when we give a simple explicit formula of the bifurcation curves on the （λ，ρ）-plane, where ρ=min_{x\in (0,1)}u(x). We also study asymptotic behavior of the bifurcation curve for f being asymptotically of the form left or right as u rightarrow infty or infty or 0^{+} or 0^{-}.