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.

A monotonicity result under symmetry and Morse index constraints in the plane / Gladiali, F.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - (2020), pp. 1-31. [10.1017/prm.2020.43]

A monotonicity result under symmetry and Morse index constraints in the plane

Gladiali F.
2020-01-01

Abstract

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.
A monotonicity result under symmetry and Morse index constraints in the plane / Gladiali, F.. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - (2020), pp. 1-31. [10.1017/prm.2020.43]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/240783
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