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Three solutions for a nonlinear Neumann boundary value problem

Volume 41 / 2014

Najib Tsouli, Omar Chakrone, Omar Darhouche, Mostafa Rahmani Applicationes Mathematicae 41 (2014), 257-266 MSC: 35J20, 35J66, 58E30. DOI: 10.4064/am41-2-13

Abstract

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.

Authors

  • Najib TsouliDepartment of Mathematics
    University Mohamed I
    P.O. Box 717
    Oujda 60000, Morocco
    e-mail
  • Omar ChakroneDepartment of Mathematics
    University Mohamed I
    P.O. Box 717
    Oujda 60000, Morocco
    e-mail
  • Omar DarhoucheDepartment of Mathematics
    University Mohamed I
    P.O. Box 717
    Oujda 60000, Morocco
    e-mail
  • Mostafa RahmaniDepartment of Mathematics
    University Mohamed I
    P.O. Box 717
    Oujda 60000, Morocco
    e-mail

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