A sharp oscillation property involving the critical Sobolev exponent for a class of superlinear elliptic problems
Published online by Cambridge University Press: 03 December 2013
Abstract
This paper studies the asymptotic behaviour as α := u(0) ↑∞ of the first zero R(α) of the radially symmetric solution of the semilinear equation
in ℝn, n ≥ 1, where h > 0 and β > 1. We establish that R(α) = O(α−(β−1)/2) if n = 1, 2 or n ≥ 3 and β < (n + 2)/(n − 2), and conjecture that lim inf α→∞R(α) > 0 if n ≥ 3 and β > (n + 2)/(n − 2).
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1303 - 1320
- Copyright
- Copyright © Royal Society of Edinburgh 2013
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