Some oscillatory properties of second order non linear differential equations

1967 ◽  
Vol 77 (1) ◽  
pp. 179-191 ◽  
Author(s):  
Marko Švec
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Oscillatory Properties

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals The differential equations of ballistics

1933 ◽  
Vol 231 (694-706) ◽  
pp. 263-288
Keyword(s):  
Differential Equations ◽  
Applied Mathematics ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Pressure Index ◽  
Internal Ballistics ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The differential equations arising in most branches of applied mathematics are linear equations of the second order. Internal ballistics, which is the dynamics of the motion of the shot in a gun, requires, except with the simplest assumptions, the discussion of non-linear differential equations of the first and second orders. The writer has shown in a previous paper* how such non-linear equations arise when the pressure-index a in the rate-of-burning equation differs from unity, although only the simplified case of non-resisted motion was there considered. It is proposed in the present investigation to examine some cases of resisted motion taking the pressure-index equal to unity, to give some extensions of the previous work, and to consider, so far as is possible, the nature and the solution of the types of differential equations which arise.

Uniformly almost periodic solutions of non-linear differential equations of the second order I. General exposition

1955 ◽  
Vol 51 (4) ◽  
pp. 604-613
Author(s):  
Chike Obi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential ◽  
The Given ◽  
Analytical Expressions

1·1. A general problem in the theory of non-linear differential equations of the second order is: Given a non-linear differential equation of the second order uniformly almost periodic (u.a.p.) in the independent variable and with certain disposable constants (parameters), to find: (i) the non-trivial relations between these parameters such that the given differential equation has a non-periodic u.a.p. solution; (ii) the number of periodic and non-periodic u.a.p. solutions which correspond to each such relation; and (iii) explicit analytical expressions for the u.a.p. solutions when they exist.

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.

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