Variability of all solutions of linear differential equations of odd order

1980 ◽  
Vol 28 (4) ◽  
pp. 742-744
Author(s):  
T. A. Chanturiya
2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles

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.


1991 ◽  
Vol 117 (3-4) ◽  
pp. 215-223 ◽  
Author(s):  
A. S. A. Al-Hammadi

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. Theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.


Author(s):  
Ch. G. Philos

SynopsisThis paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined bywhere r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.


1968 ◽  
Vol 11 (5) ◽  
pp. 743-745 ◽  
Author(s):  
T.A. Burton

In [1] Demidovic considered a system of linear differential equationswith A(t) continuous, T-periodic, odd, and skew symmetric. He proved that all solutions of (1) are either T-periodic or 2T-periodic0 In [2] Epstein used Floquet theory to prove that all solutions of (1) are T-periodic without the skew symmetric hypothesis. Epstein's results were then generalized by Muldowney in [7] using Floquet theory. Much of the above work can also be interpreted as being part of the general framework of autosynartetic systems discussed by Lewis in [5] and [6]. According to private correspondence with Lewis it seems that he was aware of these results well before they were published. However, it appears that these theorems were neither stated nor suggested in the papers by Lewis.


Author(s):  
Paul W. Spikes

SynopsisSufficient conditions are given to insure that all solutions of a perturbed non-linear second-order differential equation have certain integrability properties. In addition, some continuability and boundedness results are given for solutions of this equation.


2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Mervan Pašić ◽  
Satoshi Tanaka

We derive some simple sufficient conditions on the amplitude , the phase and the instantaneous frequency such that the so-called chirp function is fractal oscillatory near a point , where and is a periodic function on . It means that oscillates near , and its graph is a fractal curve in such that its box-counting dimension equals a prescribed real number and the -dimensional upper and lower Minkowski contents of are strictly positive and finite. It numerically determines the order of concentration of oscillations of near . Next, we give some applications of the main results to the fractal oscillations of solutions of linear differential equations which are generated by the chirp functions taken as the fundamental system of all solutions.


Author(s):  
Ian Knowles

SynopsisLet d denote the dimension of the vector space consisting of all solutions of the equation − (p(t)y′)′ + q(t)y = 0, a ≤ t < ∞; that lie in the function space L2[a, ∞). By means of certain bounds on the solutions of this equation, sufficiency criteria are obtained for the cases d = 0 and d = 2.


Author(s):  
M. S. P. Eastham

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. The theory is applied to the evaluation of the deficiency indicesN+andN−associated with symmetric differential expressions of odd order. General conditions on the coefficients are given under which all possible values ofN+andNsubject to |N+−N| ≦ 1 are realized.


Sign in / Sign up

Export Citation Format

Share Document