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arXiv · 1609.01269

On finite Morse index solutions to the quadharmonic Lane-Emden equation

Senping Luo·Juncheng Wei·Wenming Zou
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Abstract

In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic Lane-Emden equation, derive a monotonicity formula and classify the finite Morse index solution to the following quadharmonic Lane-Emden equation: \noindent \begin{equation}\nonumber \Delta^4 u=|u|^{p-1}u\;\;\;\;\hbox{in}\;\;\;\;\; \R^n. \end{equation} As a byproduct, we also get a monotonicity formula for the quadharmonic maps $ \Delta^4 u=0$.

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Senping Luo, Juncheng Wei, Wenming Zou. 2016-09-05. On finite Morse index solutions to the quadharmonic Lane-Emden equation. https://arxiv.org/abs/1609.01269

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