In this note we give existence results for the generalized Tricomi equations \({\mathcal {R}}u'' + {\mathcal {B}}u = f\) and \(({\mathcal {R}}u')' + {\mathcal {B}}u = f\) with suitable boundary data where \({\mathcal {R}}\) may be an operator (or a function) depending also on time assuming positive, null and negative sign, while \({\mathcal {B}}\) is an elliptic operator. To do that we also extend a result for equations like \(({\mathcal {R}}u')' + {\mathcal {A}}u' + {\mathcal {B}}u = f\) to equations like \({\mathcal {R}}u'' + {\mathcal {A}}u' + {\mathcal {B}}u = f\) and use these to derive the existence for the generalised Tricomi type equations mentioned above.

在本说明中，我们给出了广义Tricomi方程\（{\ mathcal {R}} u''+ {\ mathcal {B}} u = f \）和\（（{{mathcal {R}} u' ）'+ {\ mathcal {B}} u = f \）具有合适的边界数据，其中\（{\ mathcal {R}} \）可能是一个运算符（或一个函数），也取决于时间（假定正，空和负）符号，而\（{\ mathcal {B}} \）是椭圆运算符。为此，我们还将\（（{{mathcal {R}} u'）'+ {\ mathcal {A}} u'+ {\ mathcal {B}} u = f \）等式的结果扩展到方程式像\（{\ mathcal {R}} u''+ {\ mathcal {A}} u'+ {\ mathcal {B}} u = f \），并使用它们来推导上述广义Tricomi型方程的存在性以上。