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

Senping Luo; Juncheng Wei; Wenming Zou

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

Analysis of PDEs 2016-09-06 v1

Authors: Senping Luo , Juncheng Wei , Wenming Zou

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 $\Delta^4 u=0$ .

Keywords

finite Morse index quadharmonic Lane-Emden equation Joseph-Lundgren exponent monotonicity formula classification of solutions

Cite

@article{arxiv.1609.01269,
  title  = {On finite Morse index solutions to the quadharmonic Lane-Emden equation},
  author = {Senping Luo and Juncheng Wei and Wenming Zou},
  journal= {arXiv preprint arXiv:1609.01269},
  year   = {2016}
}

Comments

53 pages; comments are welcome. arXiv admin note: text overlap with arXiv:1607.04719

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