Geodesic
Bifurcation along curves for the $p$-Laplacian with radial symmetry
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a97/}
}
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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/