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

Tetsutaro Shibata

Abstract and Applied Analysis, 2005, vol. 2005, issue 6, 563-573

Abstract: 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 : = {x ∈ RN : |x| 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:=‖uλ‖2.

Date: 2005
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https://doi.org/10.1155/AAA.2005.563

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:6:p:563-573

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