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35p30 (primary)

Bulletin of the London Mathematical Society (1)

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PRECISE SPECTRAL ASYMPTOTICS FOR LOGISTIC EQUATIONS OF POPULATION DYNAMICS
TETSUTARO SHIBATA
Journal:

Bulletin of the London Mathematical Society / Volume 36 / Issue 1 / January 2004

Published online by Cambridge University Press:

23 December 2003, pp. 59-64

Print publication:

January 2004
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The semilinear elliptic eigenvalue problem with superlinear pure power nonlinearity is considered. This problem is treated from the standpoint of $L^2$-theory and the precise asymptotic formula for the eigenvalue parameter $\lambda \,{=}\, \lambda(\alpha)$ as $\alpha \,{\to}\, \infty$ is established, where $\alpha$ is the $L^2$-norm of the solution $u$ associated with $\lambda$.