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