A global bifurcation result of a Neumann problem with indefinite weight

A. El Khalil, 3-1390, Boul. Décaire Montreal (Qc) H4L 3N1, Canada
M. Ouanan, Dhar-Mahraz, Atlas-Fes, Fes, Morocco

E. J. Qualitative Theory of Diff. Equ., No. 9. (2004), pp. 1-14.

Abstract: This paper is concerned with the bifurcation result of nonlinear Neumann problem
$$
\left\{\begin{array}{lll}
-\Delta_p u=& \lambda m(x)|u|^{p-2}u + f(\lambda,x,u)& \mbox{in} \ \Omega\\
\frac{\partial u}{\partial \nu}\hspace*{0.55cm}= & 0 & \mbox{on}
\ \partial\Omega.
\end{array}
\right.
$$
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.

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