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arXiv · 1903.02385

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

Rupert L. Frank·Tobias König
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Abstract

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

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Rupert L. Frank, Tobias König. 2019-03-06. Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. https://arxiv.org/abs/1903.02385

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