English

Positive or sign-changing solutions for a critical semilinear nonlocal equation

Analysis of PDEs 2016-05-04 v1

Abstract

We consider the following critical semilinear nonlocal equation involving the fractional Laplacian (Δ)su=K(x)u2s2u,  in  RN, (-\Delta)^su=K(|x|)|u|^{2^*_s-2}u,\ \ \hbox{in}\ \ \mathbb{R}^N, where K(x)K(|x|) is a positive radial function, N>2+2sN>2+2s, 0<s<10<s<1, and 2s=2NN2s2^*_s=\frac{2N}{N-2s}. Under some asymptotic assumptions on K(x)K(x) at an extreme point, we show that this problem has infinitely many non-radial positive or sign-changing solutions.

Keywords

Cite

@article{arxiv.1511.06854,
  title  = {Positive or sign-changing solutions for a critical semilinear nonlocal equation},
  author = {Wei Long and Jing Yang},
  journal= {arXiv preprint arXiv:1511.06854},
  year   = {2016}
}