A global bifurcation result of a Neumann problem with indefinite weight

Abstract

This paper is concerned with the bifurcation result of nonlinear Neumann problem \begin{equation} \left\{\begin{array}{lll} -\Delta_p u=& \lambda m(x)|u|^{p-2}u + f(\lambda,x,u)& \mbox{in} \ \Omega\\ \frac{\partial u}{\partial \nu}\hspace{0.55cm}= & 0 & \mbox{on} \ \partial\Omega. \end{array} \right. \end{equation} We prove that the principal eigenvalue $\lambda_1$ of the corresponding eigenvalue problem with $f\equiv 0,$ is a bifurcation point by using a generalized degree type of Rabinowitz.