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In this paper, the first boundary value problem for quasilinear equation of the form △A(u, x) + m∑i=1(e)bi(u,x)/(e)xi+c(u,x)=0,Au(u,x)≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.