Article Dans Une Revue Rendiconti Lincei. Matematica e Applicazioni Année : 2019

Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

Résumé

We consider positive solutions u of the semilinear biharmonic equation ∆^2 u = |x|^-(n+4)/2 g(IxI^(n-4)/2 u in R^n\{0} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity g, we show that |x|^(n-4)2 u is a periodic function of ln |x| and we classify all such solutions.

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Dates et versions

hal-03505322 , version 1 (30-12-2021)

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Rupert L Frank, Tobias König. Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Rendiconti Lincei. Matematica e Applicazioni, 2019, 30 (4), pp.817-846. ⟨10.4171/RLM/871⟩. ⟨hal-03505322⟩
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