Geodesic
Weak solutions for the \(p\)-Laplacian with a nonlinear boundary condition at resonance
Electronic journal of differential equations, Tome 2003 (2003)
We study the existence of weak solutions to the equation

$ \Delta_p u = |u|^{p-2} u+f(x,u) $

with the nonlinear boundary condition

$ |\nabla u|^{p-2} \frac{\partial u}{\partial\nu} = \lambda |u|^{p-2} u -h(x,u)\,. $

We assume Landesman-Lazer type conditions and use variational arguments to prove the existence of solutions.
Classification : 35P05, 35J60, 35J55
Keywords: p-Laplacian, nonlinear boundary conditions, resonance 
@article{EJDE_2003__2003__a36,
     author = {Mart{\'\i}nez,  Sandra and Rossi,  Julio D.},
     title = {Weak solutions for the {\(p\)-Laplacian} with a nonlinear boundary condition at resonance},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1033.35078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a36/}
}
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AU  - Rossi,  Julio D.
TI  - Weak solutions for the \(p\)-Laplacian with a nonlinear boundary condition at resonance
JO  - Electronic journal of differential equations
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VL  - 2003
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a36/
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ID  - EJDE_2003__2003__a36
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%A Rossi,  Julio D.
%T Weak solutions for the \(p\)-Laplacian with a nonlinear boundary condition at resonance
%J Electronic journal of differential equations
%D 2003
%V 2003
%U http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a36/
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%F EJDE_2003__2003__a36
Martínez,  Sandra; Rossi,  Julio D. Weak solutions for the \(p\)-Laplacian with a nonlinear boundary condition at resonance. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a36/