Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball
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|<R}(N≥1), 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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.563 |
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| Summary: | 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|<R}(N≥1), 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:=‖uλ‖2. |
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| ISSN: | 1085-3375 1687-0409 |