Geodesic
Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions
Electronic Journal of Differential Equations, Tome 2008 (2008).

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

Summary: Using a recent result by Bonanno [2], we obtain a multiplicity result for the quasilinear elliptic problem $$\displaylines{ - \Delta_p u + |u|^{p-2}u = \lambda f(u) \quad \hbox{in } \Omega, \cr |\nabla u|^{p-2} \frac{\partial u}{\partial \nu} = \mu g(u) \quad \hbox{on } \partial\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb R^N, N \geq 3$ with smooth boundary $\partial\Omega, \frac{\partial}{\partial\nu}$ is the outer unit normal derivative, the functions $f, g$ are $(p-1)$-sublinear at infinity $(1$ and $\mu$ are positive parameters.
Classification : 35J65, 35J20
Keywords: multiple solutions, quasilinear elliptic problems, nonlinear boundary conditions 
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     author = {Chung, Nguyen Thanh},
     title = {Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a85/}
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Chung, Nguyen Thanh. Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a85/