Bifurcation along curves for the p-laplacian with radial symmetry

Francois Genoud

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7 Citations (Scopus)

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 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
Volume2012
Publication statusPublished - 2012

Keywords

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

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