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Frank, Rupert L. and König, Tobias (2019): CLASSIFICATION OF POSITIVE SINGULAR SOLUTIONS TO A NONLINEAR BIHARMONIC EQUATION WITH CRITICAL EXPONENT. In: Analysis & Pde, Vol. 12, No. 4: pp. 1101-1113

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Abstract

For n >= 5, we consider positive solutions u of the biharmonic equation Delta(2)u = u((n+4)/(n-4)) on R-n \ {0}, with a nonremovable singularity at the origin. 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 periodic functions obtained in this way. This result is relevant for the description of the asymptotic behavior of local solutions near singularities and for the Q-curvature problem in conformal geometry.

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