scholarly journals Introduction to diffusive logistic equations in population dynamics

2002 ◽  
Vol 9 (2) ◽  
Author(s):  
Kazuaki Taira
Keyword(s):  
Population Dynamics ◽  
Logistic Equations

scholarly journals Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball

2005 ◽  
Vol 2005 (6) ◽  
pp. 563-573
Author(s):  
Tetsutaro Shibata
Keyword(s):  
Population Dynamics ◽  
Eigenvalue Problem ◽  
Asymptotic Formula ◽  
Bifurcation Diagram ◽  
Global Structure ◽  
Spectral Asymptotics ◽  
Point Of View ◽  
Logistic Equations ◽  
Semilinear Elliptic ◽  
Precise Asymptotic

We consider the semilinear elliptic eigenvalue problem−Δu+k(|x|)up=λu,u>0inBR,u=0on∂BR, wherep>1is a constant,BR:={x∈RN:|x|<R}(N≥1), andλ>0is a parameter. We investigate the global structure of the branch of(λ,uλ)of bifurcation diagram from a point of view ofL2-theory. To do this, we establish a precise asymptotic formula forλ=λ(α)asα→∞, whereα:=‖uλ‖2.

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