Uniqueness of nodal radial solutions superlinear elliptic equations in a ball
Published online by Cambridge University Press: 12 November 2008
Abstract
The Dirichlet problem
is considered, where B = {x ∈ ℝN : |x| < 1}, N ≥ 3, p > 1, K ∈ C2[0, 1] and K(r) > 0 for 0 ≤ r ≤ 1. A sufficient condition is derived for the uniqueness of radial solutions of (*) possessing exactly k − 1 nodes, where k ∈ ℕ. It is also shown that there exists K ∈ C∞[0, 1] such that (*) has at least three radial solutions possessing exactly k − 1 nodes, in the case 1 < p < (N + 2)/(N − 2).
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 6 , December 2008 , pp. 1331 - 1343
- Copyright
- Copyright © Royal Society of Edinburgh 2008
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