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Browsing by Subject "variable exponent Sobolev spaces"

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    Item type:Article, Access status: Open Access ,
    On the Steklov problem involving the p(x)-Laplacian with indefinite weight
    (Wydawnictwa AGH, 2017) Ali, Khaled Ben; Ghanmi, Abdeljabbar; Kefi, Khaled
    Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the $p(x)$-Laplacian $\begin{cases}\Delta_{p(x)}u=a(x)|u|^{p(x)-2}u \quad \text{in }\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda V(x)|u|^{q(x)-2}u \quad \text{on }\partial \Omega.\end{cases}$ Our approach is based on min-max method and Ekeland's variational principle.