# Global Bifurcation for Fractional $p$-Laplacian and an Application

### Leandro M. Del Pezzo

Universidad Torcuato di Tella, C. A. de Buenos Aires, Argentina### Alexander Quaas

Universidad Técnica Federico Santa María, Valparaíso, Chile

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## Abstract

We prove the existence of an unbounded branch of solutions to the non-linear non-local equation

bifurcating from the first eigenvalue. Here $(-\Delta)^s_p$ denotes the fractional $p$-Laplacian and $\Omega\subset\mathbb R^n$ is a bounded regular domain. The proof of the bifurcation results relies in computing the Leray–Schauder degree by making an homotopy respect to $s$ (the order of the fractional $p$-Laplacian) and then to use results of local case (that is $s=1$) 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 $p$-Laplacian and an Application. Z. Anal. Anwend. 35 (2016), no. 4, pp. 411–447

DOI 10.4171/ZAA/1572