Geodesic
Bifurcation along curves for the \(p\)-Laplacian with radial symmetry
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 35J66, 35J92, 35B32
Keywords: Dirichlet problem, radial p-Laplacian, bifurcation, solution curve 
@article{EJDE_2012__2012__a97,
     author = {Genoud,  Francois},
     title = {Bifurcation along curves for the {\(p\)-Laplacian} with radial symmetry},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1258.35103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a97/}
}
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VL  - 2012
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%A Genoud,  Francois
%T Bifurcation along curves for the \(p\)-Laplacian with radial symmetry
%J Electronic journal of differential equations
%D 2012
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%F EJDE_2012__2012__a97
Genoud,  Francois. Bifurcation along curves for the \(p\)-Laplacian with radial symmetry. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a97/