Geodesic
Multiple solutions for the \(p\)-Laplace equation with nonlinear boundary conditions
Electronic journal of differential equations, Tome 2006 (2006)
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},
     year = {2006},
     volume = {2006},
     zbl = {1166.35328},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a182/}
}
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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/