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We have also proved that these solutions are in $L^{\\infty}(\\Omega)$. \\begin{align*} \\begin{split} -\\Delta_{p(x,y)}^{s(x,y)}u &= \\beta|u|^{\\alpha(x)-2}u+\\lambda f(x,u)\\,\\,\\mbox{in}\\,\\,\\Omega,\\\\ u &= 0\\,\\, \\mbox{in}\\,\\, \\mathbb{R}^{N}\\setminus\\Omega \\end{split} \\end{align*} Here, $\\lambda, \\beta > 0$ are parameters and $f(x,u)$ is a general nonlinear term satisfying certain conditions. 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Choudhuri","submitted_at":"2019-07-21T17:23:21Z","abstract_excerpt":"In this paper we study the existence and multiplicity of two distinct nontrivial weak solutions of the following equation in Nehari manifold. We have also proved that these solutions are in $L^{\\infty}(\\Omega)$. \\begin{align*} \\begin{split} -\\Delta_{p(x,y)}^{s(x,y)}u &= \\beta|u|^{\\alpha(x)-2}u+\\lambda f(x,u)\\,\\,\\mbox{in}\\,\\,\\Omega,\\\\ u &= 0\\,\\, \\mbox{in}\\,\\, \\mathbb{R}^{N}\\setminus\\Omega \\end{split} \\end{align*} Here, $\\lambda, \\beta > 0$ are parameters and $f(x,u)$ is a general nonlinear term satisfying certain conditions. 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