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A monotonicity result under symmetry and Morse index constraints in the plane
Published online by Cambridge University Press: 21 July 2020
Abstract
This paper deals with solutions of semilinear elliptic equations of the type
\[ \left\{\begin{array}{@{}ll} -\Delta u = f(|x|, u) \qquad & \text{ in } \Omega, \\ u= 0 & \text{ on } \partial \Omega, \end{array} \right. \]
$e\in \mathcal {S}$ such that u is symmetric with respect to e and it is strictly monotone in the angular variable in a sector of angle θ/2. The result applies to least-energy and nodal least-energy solutions in spaces of functions invariant by rotations and produces multiplicity results.
Keywords
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 885 - 915
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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