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

Tetsutaro Shibata

Abstract and Applied Analysis, 2005, vol. 2005, 1-11

Abstract:

We consider the semilinear elliptic eigenvalue problem − Δ u + k ( | x | ) u p = λ u , u > 0 in B R , u = 0 on ∂ B R , where p > 1 is a constant, B R : = { x ∈ R N : | x | < R } ( N ≥ 1 ) , and λ > 0 is a parameter. We investigate the global structure of the branch of ( λ , u λ ) of bifurcation diagram from a point of view of L 2 -theory. To do this, we establish a precise asymptotic formula for λ = λ ( α ) as α → ∞ , where α : = ‖ u λ ‖ 2 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:247927

DOI: 10.1155/AAA.2005.563

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