scholarly journals A new proof of multisummability of formal solutions of non linear meromorphic differential equations

1994 ◽  
Vol 44 (3) ◽  
pp. 811-848 ◽  
Author(s):  
Jean-Pierre Ramis ◽  
Yasutaka Sibuya
Keyword(s):  
Differential Equations ◽  
Non Linear ◽  
Formal Solutions ◽  
Meromorphic Differential

scholarly journals Invariants for reducible systems of meromorphic differential equations

1980 ◽  
Vol 23 (2) ◽  
pp. 163-186 ◽  
Author(s):  
W. Balser ◽  
W. B. Jurkat ◽  
D. A. Lutz
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Coefficient Matrix ◽  
Analytic Solutions ◽  
Irregular Singular Point ◽  
Formal Solutions ◽  
The Given ◽  
Meromorphic Differential

With differential equations in the neighbourhood of an irregular singular point, it sometimes happens that formal solutions may converge. For example, this occurs for Bessel's equation at∞ when the parameter is half of an odd integer. In addition, there are some classical theorems of Perron and Lettenmeyer which give sufficient conditions for the existence of linearly independent analytic solutions at (generally) an irregular singular point. Using the principle of reduction of order, such a solution may be used to transform the differential equation into one whose coefficient matrix is triangularly blocked with an (n – 1) and 1-block on the diagonal. The solutions of the given differential equation can thus be obtained by solving a lower dimensional differential equation plus quadrature.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

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