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We prove that the solution of the equation with initial value \\lambda u_{p,K} blows up in finite time if |\\lambda-1|>0 is sufficiently small and if p is sufficiently large. The proof is based on the analysis of the asymptotic behavior of $u_{p,K}$ and of the linearized operator L= -\\Delta - p |u_{p,K}|^{p-1}. 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