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Frank, Rupert L. and König, Tobias (2019): Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. In: Rendiconti Lincei-Matematica E Applicazioni, Vol. 30, No. 4: pp. 817-846

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Abstract

We consider positive solutions u of the semilinear biharmonic equation Delta(2)u = vertical bar x vertical bar(n+4/2) g(vertical bar x vertical bar(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 vertical bar x vertical bar(n-4/2)u is a periodic function of ln vertical bar x vertical bar and we classify all such solutions.

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