Peak Solutions for the fractional Nirenberg problem

Abstract

In this paper, the fractional order curvature equation $(-\Delta {)}^{\gamma }u=(1+\epsilon K(x))u^{\frac{N+2\gamma }{N-2\gamma }}$ in ${\mathbb{R}}^N$ is considered. Assuming $K(x)$ has two critical points satisfying certain local conditions, we prove the existence of two-peak solutions.

References in corpus (3)

• On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
• On a fractional Nirenberg problem, part II: existence of solutions
• The Nirenberg problem and its generalizations: A unified approach