Geodesic
Weak solutions for the $p$-Laplacian with a nonlinear boundary condition at resonance
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: 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},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a36/}
}
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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/