This paper deals with solutions of semilinear elliptic equations of the type where ω is a radially symmetric domain of the plane that can be bounded or unbounded. We consider solutions u that are invariant by rotations of a certain angle θ and which have a bound on their Morse index in spaces of functions invariant by these rotations. We can prove that or u is radial, or, else, there exists a direction 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.
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Titolo: | A monotonicity result under symmetry and Morse index constraints in the plane |
Autori: | GLADIALI, Francesca Maria (Corresponding) |
Data di pubblicazione: | 2020 |
Rivista: | |
Handle: | http://hdl.handle.net/11388/240783 |
Appare nelle tipologie: | 1.1 Articolo in rivista |