We prove the existence of an unbounded branch of solutions to the non-linear non-local equation
bifurcating from the first eigenvalue. Here denotes the fractional -Laplacian and is a bounded regular domain. The proof of the bifurcation results relies in computing the Leray–Schauder degree by making an homotopy respect to (the order of the fractional -Laplacian) and then to use results of local case (that is ) found in the paper of del Pino and Manásevich [J. Diff. Equ. 92 (1991)(2), 226–251]. Finally, we give some application to an existence result.
Cite this article
Leandro M. Del Pezzo, Alexander Quaas, Global Bifurcation for Fractional -Laplacian and an Application. Z. Anal. Anwend. 35 (2016), no. 4, pp. 411–447DOI 10.4171/ZAA/1572