Local models of the greatest characteristic exponent of differential equations depending on parameters (Q1118744)

The differential equation \(a_ 0(\lambda)y^{(n)}+a_ 1(\lambda)y^{(n-1)}+...+a_ n(\lambda)y=0\) is considered, where \(a_ i\in C^{\infty}(\Lambda)\), \(\Lambda\) is a differentiable manifold of finite dimension. The singularities of the greatest characteristic exponent of the equation are classified. It is proved that the number of local models possible for f(\(\lambda)\) is finite, even the list of the models is given.