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PRECISE SPECTRAL ASYMPTOTICS FOR LOGISTIC EQUATIONS OF POPULATION DYNAMICS

Published online by Cambridge University Press:  23 December 2003

TETSUTARO SHIBATA
TETSUTARO SHIBATA
Affiliation:
The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japanshibata@mis.hiroshima-u.ac.jp
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Abstract

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 $\lambda$.

Keywords

35P30 (primary)35J60 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 1 , January 2004 , pp. 59 - 64
Copyright
© The London Mathematical Society 2004

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