Abstract and Applied Analysis
Volume 2005 (2005), Issue 6, Pages 563-573
Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball
Applied Mathematics Research Group, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8527, Japan
Received 17 August 2004
Copyright © 2005 Tetsutaro Shibata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the semilinear elliptic eigenvalue problem , in , on , where is a constant, , and is a parameter. We investigate the global structure of the branch of of bifurcation diagram from a point of view of -theory. To do this, we establish a precise asymptotic formula for as , where .