We consider the nonlinear eigenvalue problem
where is a parameter. It is known that under some conditions on , the shape of the solutions associated with is almost `box' when . The purpose of this paper is to study precisely the asymptotic shape of the solutions as from a standpoint of -framework. To do this, we establish the asymptotic formulas for -norm of the solutions as .
Submitted January 11, 2005. Published March 29, 2005.
Math Subject Classifications: 34B15.
Key Words: Asymptotic formula; -norm; simple pendulum; logistic equation
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| Tetsutaro Shibata |
Department of Applied Mathematics
Graduate School of Engineering
Higashi-Hiroshima, 739-8527, Japan
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