Bifurcation along curves for the p-laplacian with radial symmetry

Francois Genoud*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 R-N, N >= 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.

Original languageEnglish
Article number124
Number of pages17
JournalElectronic Journal of Differential Equations
Publication statusPublished - 2012


  • Dirichlet problem
  • radial p-Laplacian
  • bifurcation
  • solution curve


Dive into the research topics of 'Bifurcation along curves for the p-laplacian with radial symmetry'. Together they form a unique fingerprint.

Cite this