Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 124, pp. 1-17.
Title: Bifurcation along curves for the p-Laplacian with radial symmetry
Authors: Francois Genoud (Heriot-Watt Univ., U. K.)
Abstract:
We study the global structure of the set of radial solutions of a nonlinear
Dirichlet eigenvalue problem involving the p-Laplacian with p>2, in the unit
ball of $\mathbb{R}^N$, $N \geq 1$. We show that all non-trivial radial
solutions lie on smooth curves of respectively positive and negative solutions,
bifurcating from the first eigenvalue of a weighted p-linear problem.
Our approach involves a local bifurcation result of Crandall-Rabinowitz type,
and global continuation arguments relying on monotonicity properties of the
equation.
An important part of the analysis is dedicated to the delicate issue of
differentiability of the inverse p-Laplacian, and holds for all p>1.
Submitted March 7, 2012. Published July 31, 2012.
Math Subject Classifications: 35J66, 35J92, 35B32.
Key Words: Dirichlet problem; radial p-Laplacian; bifurcation; solution curve.