Approximate determination of periodic solutions of a class of non-linear differential equations

1972 ◽  
Vol 7 (2) ◽  
pp. 207-220 ◽  
Author(s):  
Jagdish Chandra ◽  
B.A. Fleishman
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Linear Differential Equations ◽  
Approximate Determination ◽  
Non Linear ◽  
Linear Differential

Periodic solutions of non-linear differential equations of the second order. V

1951 ◽  
Vol 47 (4) ◽  
pp. 752-755 ◽  
Author(s):  
Chike Obi
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

1·1. Let van der Pol's equation be taken in the formwhere ε1, ε2, k1 and k2 are small, and ω ≠ 0 is a constant, rational or irrational, independent of them.

Periodic solutions of non-linear differential equations of the second order. IV

1951 ◽  
Vol 47 (4) ◽  
pp. 741-751 ◽  
Author(s):  
Chike Obi
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Theoretical Investigation ◽  
Linear Differential Equations ◽  
The Real ◽  
Subharmonic Solutions ◽  
Real Domain ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

1.1. This paper is a theoretical investigation in the real domain of the existence of subharmonic solutions of non-linear differential equations of the formwhere F is analytic and of least period 2π/ω in t; ε = (ε1, …, εn) is small; and F(x, ẋ, 0, t) is not linear in x and ẋ.

On The Motion of Three Vortices

1949 ◽  
Vol 1 (3) ◽  
pp. 257-270 ◽  
Author(s):  
J. L. Synge
Keyword(s):  
Differential Equations ◽  
Incompressible Fluid ◽  
Linear Differential Equations ◽  
Vortex Filaments ◽  
First Order ◽  
Perfect Incompressible Fluid ◽  
Non Linear ◽  
The Mean ◽  
Linear Differential

In a perfect incompressible fluid extending to infinity, the determination of the motion of N parallel rectilinear vortex filaments involves the solution of N non-linear differential equations, each of the first order. The method of Kirchhoff provides certain constants of the motion. If we describe the positions of the vortices by their point-traces on a plane perpendicular to them, the following facts follow from the theory of Kirchhoff:(1.1) The mean centre of the system is fixed.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

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