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• W2928172166 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. ] where $Omega$ 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 $theta$ 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 $ein mathcal S$ such that $u$ is symmetric with respect to $e$ and it is strictly monotone in the angular variable in a sector of angle $frac{theta}2$. The result applies to least-energy and nodal least-energy solutions in spaces of functions invariant by rotations and produces multiplicity results." @default.
• W2928172166 created "2019-04-11" @default.
• W2928172166 creator A5068964305 @default.
• W2928172166 date "2019-04-08" @default.
• W2928172166 modified "2023-09-27" @default.
• W2928172166 title "A monotonicity result under symmetry and Morse index constraints in the plane" @default.
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• W2928172166 hasPublicationYear "2019" @default.
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