# Mathematische Nachrichten

## Bifurcation properties for a class of fractional Laplacian equations in $\mathbit{}{\mathbb{R}}^{\mathbf{N}}$

### Abstract

This paper concerns with the study of some bifurcation properties for the following class of nonlocal problems

• (P)

where $N>2s$, $s\in \left(0,1\right)$, $\lambda >0$, $f:{\mathbb{R}}^{N}\to \mathbb{R}$ is a positive continuous function, $h:\mathbb{R}\to \mathbb{R}$ is a bounded continuous function and ${\left(-\mathrm{\Delta }\right)}^{s}u$ is the fractional Laplacian. The main tools used are the Leray–Shauder degree theory and the global bifurcation result due to Rabinowitz.

View all

View all