Abstract Under appropriate conditions, we prove that for two arbitrary solutions $$s_1 $$ and $$s_2 $$ of the Dirichlet problem lying between lower and upper functions there exists a continuous mapping $$z $$ of the interval $$[0,1] $$ into the solution set of the Dirichlet problem such that $$z(0)=s_1 $$ and $$z(1)=s_2 $$ .

中文翻译：

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下函数与上函数之间狄利克雷问题的解集是连通的

摘要 在适当的条件下，我们证明对于位于下函数和上函数之间的狄利克雷问题的两个任意解 $$s_1 $$ 和 $$s_2 $$ 存在区间 $$[0 ,1] $$ 进入狄利克雷问题的解集，使得 $$z(0)=s_1 $$ 和 $$z(1)=s_2 $$ 。