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Theoretical analysis reveals a sharp Onofri-type inequality in spherical Liouville equations, highlighting conditions for critical point existence.
We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.
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Gabriele Mancini (2015) studied this question.
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