We prove the existence of solutions for a quasilinear elliptic system$$\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\,\sigma (x,u,Du)&{}=f(x,u,Du)\quad \text {in}\;\varOmega ,\\ u&{}=0\quad \text {on}\;\partial \varOmega . \end{array} \right. \end{aligned}$$The results are obtained in Orlicz–Sobolev spaces by means of the Young measures.

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具有非标准增长且单调性较弱的拟线性椭圆系统

我们证明了拟线性椭圆系统$$ \ begin {aligned} \ left \ {\ begin {array} {ll}-\ text {div} \，\ sigma（x，u，Du）＆{}的解的存在= f（x，u，Du）\ quad \ text {in} \; \ varOmega，\\ u＆{} = 0 \ quad \ text {on} \; \ partial \ varOmega。\ end {array} \ right。\ end {aligned} $$通过Young度量在Orlicz–Sobolev空间中获得结果。