Abstract:
In this paper, we consider the bifurcation problem for fractional Laplace equation
(−Δ)su=λu+f(λ,x,u)in Ω,u=0in Rn∖Ω,
where Ω⊂Rn,n>2s(0<s<1) is an open bounded subset with smooth boundary, (−Δ)s stands for the fractional Laplacian. We show that a continuum of solutions bifurcates out from the principal eigenvalue λ1 of the eigenvalue problem
(−Δ)sv=λvinΩ,v=0inRn∖Ω,
and, conversely.