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

Tetsutaro Shibata

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 Δu+k(|x|)up=λu, u>0 in BR, u=0 on BR, where p>1 is a constant, BR:={xRN:|x|<R}(N1), and λ>0 is a parameter. We investigate the global structure of the branch of (λ,uλ) of bifurcation diagram from a point of view of L2-theory. To do this, we establish a precise asymptotic formula for λ=λ(α) as α, where α:=uλ2.