Special Session 72: Nonlinear elliptic PDEs

Structures and evolution of bifurcation diagrams of a p-Laplacian generalized logistic problem with constant yield harvesting
Shin-Hwa Wang
National Tsing Hua University, TAIWAN
Taiwan
Co-Author(s):    Kuo-Chih Hung and Jhih-Jyun Zeng
Abstract:
We study evolutionary bifurcation diagrams for a $p$-Laplacian generalized logistic problem where $p > 1$ and $\mu > 0$ is the harvesting parameter. We mainly prove that, for fixed $\mu > 0$, on the $( \lambda, \left \Vert u \right \Vert _{\infty} )$-plane, the bifurcation diagram always consists of a $\subset$-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying $\mu > 0$. We give two interesting applications. It is a joint work with Kuo-Chih Hung and Jhih-Jyun Zeng.