On Halphen and Laguerre-Forsyth canonical forms of linear differential equations
We introduce and study the sheaf of Deligne to describe singular points of a linear differential operator and we develop a technique based on homological algebra to prove index theorems for .As particular cases, we obtain index theorems for acting in spaces of multisummable series and a new proof of the index theorem of Malgrange in the space of convergent power series and of the index theorems of Ramis in the spaces of Gevrey series.We compute the values of these indices in terms of the formal...
The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.
The paper deals with the oscillation of a differential equation as well as with the structure of its fundamental system of solutions.