Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere

Daowen Lin; Xi-Nan Ma

Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere

Analysis of PDEs 2022-11-08 v1

Authors: Daowen Lin , Xi-Nan Ma

Abstract

We use the integral by parts to get a Liouville type theorem for a class quasilinear $p$ -Laplace type equation on the sphere, this $p$ -Laplace type equation arises from the study of asymptotic behavior near the origin for the semi-linear $p$ -Laplace equation on the puncture ball $B_1(o) \subset R^n$ . This gives a positive answer to L. V\'{e}ron's question in a paper \cite{Veron92} and his book \cite{Veron} at page 440.

Keywords

liouville theorem p-laplace equation sphere integral by parts asymptotic behavior puncture ball

Cite

@article{arxiv.2211.03532,
  title  = {Liouville type theorem for a class quasilinear $p$-Laplace type equation on the sphere},
  author = {Daowen Lin and Xi-Nan Ma},
  journal= {arXiv preprint arXiv:2211.03532},
  year   = {2022}
}

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