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

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