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\\\\ u=v&=& 0 & \\text{on }\\partial \\Omega ,\\\\ u,v& \\geq & 0 & \\text{in }\\Omega, \\end{array}% \\right. \\end{equation*} where $\\Omega$ is a bounded domain of $\\ren$ and $p\\ge 1$, $q>0$ with $pq>1$. $f,g$ are nonnegative measurable functions with additional hypotheses and $\\a, \\l\\ge 0$.\n  As a consequence we show that the fourth order problem \\begin{equation*} \\left\\{ 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