On the bifurcation results for fractional Laplace equations

Abstract

In this paper, we consider the bifurcation problem for the fractional Laplace equation urn:x-wiley:0025584X:media:mana201600250:mana201600250-math-0001 where urn:x-wiley:0025584X:media:mana201600250:mana201600250-math-0002 is an open bounded subset with smooth boundary, urn:x-wiley:0025584X:media:mana201600250:mana201600250-math-0003 stands for the fractional Laplacian. We show that a continuum of solutions bifurcates out from the principal eigenvalue λ1 of the problem urn:x-wiley:0025584X:media:mana201600250:mana201600250-math-0004 and, conversely.