Existence of solutions entering at a singular point of an autonomous system having a formal solution

1990 ◽  
Vol 23 (4) ◽  
pp. 308-317 ◽  
Author(s):  
A. N. Kuznetsov
2007 ◽  
Vol 143 (6) ◽  
pp. 1465-1477
Author(s):  
João Pedro Pinto dos Santos

AbstractIn the complex domain, one can integrate (solve) holomorphic ordinary differential equations (ODEs) near a non-singular point. We study the existence of solutions in the case of a positive characteristic base field k which is complete with respect to a non-Archimedean absolute value. ODEs are substituted by modules over a ring of analytic functions endowed with an action of all differential operators. The monodromy groups associated to the corresponding category are computed.


1973 ◽  
Vol 14 (6) ◽  
pp. 1037-1042 ◽  
Author(s):  
V. A. Kondrat'ev ◽  
V. S. Samovol

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