Dwivedi, GauravGauravDwivediTyagi, JagmohanJagmohanTyagiVerma, Ram BaranRam BaranVerma2025-08-282025-08-282016-06-01http://arxiv.org/abs/1606.04452https://d8.irins.org/handle/IITG2025/20024In this paper, we consider the bifurcation problem for fractional Laplace equation (??)su=?u+f(?,x,u)in ?,u=0in 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 ?1 of the eigenvalue problem (??)sv=?vin?,v=0inRn??, and, conversely.en-USe-Printe-Print123456789/555