scholarly journals On Asymptotic Classification of Solutions to Nonlinear Third- and Fourth-Order Differential Equations with Power Nonlinearity

2015 ◽  
Author(s):  
И.В. Асташова ◽  
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Power Nonlinearity ◽  
Classification Of Solutions

scholarly journals ON ASYMPTOTIC CLASSIFICATION OF SOLUTIONS TO FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH SINGULAR POWER NONLINEARITY

2016 ◽  
Vol 21 (4) ◽  
pp. 502-521 ◽  
Author(s):  
Irina Astashova
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
All Solutions ◽  
Classification Of Solutions ◽  
Type Differential Equation

The asymptotic behavior of all solutions to the fourth-order Emden– Fowler type differential equation with singular nonlinearity is investigated. The equation is transformed into a system on the three-dimensional sphere. By investigation of the asymptotic behavior of all possible trajectories of this system an asymptotic classification of all solutions to the equation is obtained.

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