Geodesic
Three solutions for a nonlinear Neumann boundary value problem
Najib Tsouli1 ; Omar Chakrone1 ; Omar Darhouche1 ; Mostafa Rahmani1
1 Department of Mathematics University Mohamed I P.O. Box 717 Oujda 60000, Morocco
Applicationes Mathematicae, Tome 41 (2014) no. 2-3, pp. 257-266.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the $p(x$)-Laplacian of the form \begin{align*} {-}\Delta_{p(x)} u+a(x)|u|^{p(x)-2}u =\mu g(x,u)\quad \text{in } \Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda f(x,u) \quad \text{on } \partial\Omega. \end{align*} Our technical approach is based on the three critical points theorem due to Ricceri.
DOI : 10.4064/am41-2-13
Keywords: paper establish existence least three solutions nonlinear neumann boundary value problem involving laplacian form begin align* delta quad text omega nabla frac partial partial lambda quad text partial omega end align* technical approach based three critical points theorem due ricceri

Najib Tsouli 1 ; Omar Chakrone 1 ; Omar Darhouche 1 ; Mostafa Rahmani 1

1 Department of Mathematics University Mohamed I P.O. Box 717 Oujda 60000, Morocco 
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Najib Tsouli; Omar Chakrone; Omar Darhouche; Mostafa Rahmani. Three solutions for a nonlinear Neumann boundary value problem. Applicationes Mathematicae, Tome 41 (2014) no. 2-3, pp. 257-266. doi : 10.4064/am41-2-13. http://geodesic.mathdoc.fr/articles/10.4064/am41-2-13/

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