Entire nodal solutions to the pure critical exponent problem for the $p$-Laplacian

Mónica Clapp; Luis Lopez Rios

Entire nodal solutions to the pure critical exponent problem for the $p$-Laplacian

Analysis of PDEs 2017-11-13 v1

Authors: Mónica Clapp , Luis Lopez Rios

Abstract

We establish the existence of multiple sign-changing solutions to the quasilinear critical problem $-\Delta_{p} u=|u|^{p^*-2}u, \qquad u\in D^{1,p}(\mathbb{R}^{N}),$ for $N\geq4$ , where $\Delta_{p}u:=\mathrm{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$ -Laplace operator, $1<p<N$ and $p^*:=\frac{Np}{N-p}$ is the critical Sobolev exponent

Keywords

p-laplacian critical exponent sign-changing solutions sobolev space quasilinear elliptic equation

Cite

@article{arxiv.1711.03681,
  title  = {Entire nodal solutions to the pure critical exponent problem for the $p$-Laplacian},
  author = {Mónica Clapp and Luis Lopez Rios},
  journal= {arXiv preprint arXiv:1711.03681},
  year   = {2017}
}

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