JournalsrlmVol. 30, No. 4pp. 817–846

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

  • Rupert L. Frank

    Ludwig-Maximilians-Universität München, Germany and California Institute of Technology, Pasadena, USA
  • Tobias König

    Ludwig-Maximilians-Universität München, Germany
Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity cover
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Abstract

We consider positive solutions uu of the semilinear biharmonic equation Δ2u=xn+42g(xn42u)\Delta^2 u = |x|^{-\frac{n+4}{2}} g(|x|^\frac{n-4}{2} u) in Rn{0}\mathbb R^n \setminus \{0\} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity gg, we show that xn42u|x|^\frac{n-4}{2} u is a periodic function of lnx\ln |x| and we classify all such solutions.

Cite this article

Rupert L. Frank, Tobias König, Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 4, pp. 817–846

DOI 10.4171/RLM/871