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It is proved that the DSM (Dynamical Systems Method) \\bee \\dot{u}(t)=-A^{-1}_{a(t)}(u(t))[F(u(t))+a(t)u(t)-f],\\quad u(0)=u_0,\\ %\\dot{u}=\\frac{d u}{dt}, \\eee converges to $y$ as $t\\to +\\infty$, for $a(t)$ properly chosen. 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