Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains

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On the Existence and the Profile of Nodal solutions of Elliptic Equations Involving Critical Growth (2006, result): “This result has been obtained by Aftalion and Pacella in [ 1 ], using a completely different approach.”
Symmetry of solutions to semilinear elliptic equations via Morse index (2007, background): “We also show an interesting consequence of Theorem 1.1 concerning the geometrical properties of the nodal set of a sign changing solution of (1.1) which relies on some results of [ 1 ].”