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
Keyword(s):  
Singular Point ◽  
Autonomous System ◽  
Existence Of Solutions ◽  
Formal Solution

scholarly journals Local solutions to positive characteristic non-Archimedean differential equations

2007 ◽  
Vol 143 (6) ◽  
pp. 1465-1477
Author(s):  
João Pedro Pinto dos Santos
Keyword(s):  
Singular Point ◽  
Differential Equations ◽  
Analytic Functions ◽  
Differential Operators ◽  
Positive Characteristic ◽  
Existence Of Solutions ◽  
Base Field ◽  
Absolute Value ◽  
Monodromy Groups ◽  
Local Solutions

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.

The linearization of an autonomous system in the neighborhood of a ?node?-type singular point

1973 ◽  
Vol 14 (6) ◽  
pp. 1037-1042 ◽  
Author(s):  
V. A. Kondrat'ev ◽  
V. S. Samovol
Keyword(s):  
Singular Point ◽  
Autonomous System ◽  
Node Type
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