Entire sign-changing solutions with finite energy to the fractional Yamabe equation

Danilo Garrido and Monica Musso

Vol. 283 (2016), No. 1, 85–114

DOI: 10.2140/pjm.2016.283.85

Abstract

We show the existence of infinitely many finite energy sign-changing solutions for the fractional Yamabe-type equation

$${\left(-\Delta \right)}^{s}u=|u{|}^{\frac{4s}{n-2s}}u\text{ in }{ℝ}^n,$$

where $n\ge 3$ and $s\in \left(\frac{1}{2},1\right)$.

Keywords

fractional Laplacian, energy solutions, Yamabe-type equation

Mathematical Subject Classification 2010

Primary: 35J60, 35J61, 35J75, 35R11

Milestones

Received: 5 January 2015

Accepted: 22 October 2015

Published: 14 June 2016