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Hamdani","submitted_at":"2019-08-22T13:38:45Z","abstract_excerpt":"We study the existence and multiplicity results for the following nonlocal $p(x)$-Kirchhoff problem: \\begin{equation}\n  \\label{10} \\begin{cases} -\\left(a-b\\int_\\Omega\\frac{1}{p(x)}| \\nabla u| ^{p(x)}dx\\right)div(|\\nabla u| ^{p(x)-2}\\nabla u)=\\lambda |u| ^{p(x)-2}u+g(x,u) \\mbox{ in } \\Omega, \\\\ u=0,\\mbox{ on } \\partial\\Omega, \\end{cases} \\end{equation} where $a\\geq b > 0$ are constants, $\\Omega\\subset \\mathbb{R}^N$ is a bounded smooth domain, $p\\in C(\\overline{\\Omega})$ with $N>p(x)>1$, $\\lambda$ is a real parameter and $g$ is a continuous function. 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