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This analysis reveals the existence of nodal solutions on the unit sphere, indicating symmetry considerations in their behavior.
By using mountain pass arguments and a novel grouptheoretical approach, in this paper we study the existence of multiple sequences of nodal solutions with prescribed different symmetries for a wide class of (sub)critical elliptic problems settled on the unit sphere (Sd, h), of dimension d ≥ 5, whose simple prototype is given by the celebrated Yamabe equation on the sphere.
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Molica Bisci Giovanni (2025) studied this question.
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