We deal with a multiparameter Dirichlet system having the form

where \({\mathcal {M}}\) stands for the mean curvature operator in Minkowski space, \({\mathcal {B}}(R)\) is an open ball of radius R in \({\mathbb {R}}^N,\) the parameters \(\lambda _1,\lambda _2\) are positive, the functions \(\mu _1,\; \mu _2:[0,R]\rightarrow [0,\infty )\) are continuous and positive and the continuous functions \(f_1,f_2\) satisfy some sign, growth and monotonicity conditions. Among others, these type of nonlinearities, include the Lane-Emden ones. For this system we show that there exists a continuous curve \(\varGamma \) splitting the first quadrant into two disjoint unbounded, open sets \({\mathcal {O}}_1\) and \({\mathcal {O}}_2\) such that the system has zero, at least one or at least two positive radial solutions according to \((\lambda _1, \lambda _2)\in {\mathcal {O}}_1,\)\((\lambda _1, \lambda _2)\in \varGamma \) or \((\lambda _1, \lambda _2)\in {\mathcal {O}}_2,\) respectively. The set \({\mathcal {O}}_1\) is adjacent to the coordinates axes \(0 \lambda _1\) and \(0 \lambda _2\) and the curve \(\varGamma \) approaches asymptotically to two lines parallel to the axes \(0 \lambda _1\) and \(0 \lambda _2\). Actually, this result extends to more general radial systems the recent existence/non-existence and multiplicity result obtained in the case of Lane-Emden systems.

我们处理具有以下形式的多参数Dirichlet系统

其中\（{\ mathcal {M}} \）表示在闵可夫斯基空间中的平均曲率运算符，\（{\ mathcal {B}}（R）\）是半径的开口球ř在\（{\ mathbb { R}} ^ N，\）参数\（\ lambda _1，\ lambda _2 \）为正，函数\（\ mu _1，\; \ mu _2：[0，R] \ rightarrow [0，\ infty ）\）是连续和正的，并且连续函数\（f_1，f_2 \）满足某些符号，增长和单调性条件。其中，这些非线性类型包括Lane-Emden非线性。对于该系统，我们表明存在一条连续曲线\（\ varGamma \）将第一象限分为两个不相交的无边界开放集\（{\ mathcal {O}} _ 1 \）和\（{\ mathcal {O}} _ 2 \）使得系统根据\（（\ lambda _1 ）具有零个，至少一个或至少两个正径向解，\ lambda _2）\ in {\ mathcal {O}} _ 1，\）\（（\ lambda _1，\ lambda _2）\ in \ varGamma \）或\（（\ lambda _1，\ lambda _2）\ in { \ mathcal {O}} _ 2，\）。集合\（{\ mathcal {O}} _ 1 \）与坐标轴\（0 \ lambda _1 \）和\（0 \ lambda _2 \）相邻，并且曲线\（\ varGamma \）渐近地接近两个平行于轴\（0 \ lambda _1 \）和\（0 \ lambda _2 \）的线。实际上，该结果将更广泛的径向系统扩展到在Lane-Emden系统的情况下获得的最近存在/不存在和多重性结果。