Geodesic
Multiple solutions for the $p$-Laplace equation with nonlinear boundary conditions
Electronic Journal of Differential Equations, Tome 2006 (2006).

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

Summary: In this note, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation $$ -\Delta_p u + |u|^{p-2}u = f(x,u) $$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^N$ with nonlinear boundary conditions $|\nabla u|^{p-2}\frac{\partial u}{\partial\nu} = g(x,u)$ on $\partial\Omega$. The proof is based on variational arguments.
Classification : 35J65, 35J20
Keywords: p-Laplace equations, nonlinear boundary conditions, variational methods 
@article{EJDE_2006__2006__a182,
     author = {Bonder, Juli\'an Fern\'andez},
     title = {Multiple solutions for the $p${-Laplace} equation with nonlinear boundary conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a182/}
}
TY  - JOUR
AU  - Bonder, Julián Fernández
TI  - Multiple solutions for the $p$-Laplace equation with nonlinear boundary conditions
JO  - Electronic Journal of Differential Equations
PY  - 2006
VL  - 2006
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a182/
LA  - en
ID  - EJDE_2006__2006__a182
ER  - 
%0 Journal Article
%A Bonder, Julián Fernández
%T Multiple solutions for the $p$-Laplace equation with nonlinear boundary conditions
%J Electronic Journal of Differential Equations
%D 2006
%V 2006
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a182/
%G en
%F EJDE_2006__2006__a182
Bonder, Julián Fernández. Multiple solutions for the $p$-Laplace equation with nonlinear boundary conditions. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a182/