Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 124, pp. 117.
Bifurcation along curves for the pLaplacian with radial symmetry
Francois Genoud
Abstract:
We study the global structure of the set of radial solutions of a nonlinear
Dirichlet eigenvalue problem involving the pLaplacian with p>2, in the unit
ball of
,
.
We show that all nontrivial radial
solutions lie on smooth curves of respectively positive and negative solutions,
bifurcating from the first eigenvalue of a weighted plinear problem.
Our approach involves a local bifurcation result of CrandallRabinowitz 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 pLaplacian, 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 pLaplacian; bifurcation; solution curve.
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François Genoud
Department of Mathematics and
the Maxwell Institute for Mathematical Sciences
HeriotWatt University
Edinburgh EH14 4AS, United Kingdom
email: F.Genoud@hw.ac.uk

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