On the bifurcation results for fractional Laplace equations

In this paper, we consider the bifurcation problem for the fractional Laplace equation (Formula presented.) where Ω ⊂ 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 λ<inf>1</inf> of the problem (Formula presented.) and, conversely.