Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
comparison theorem; advanced argument; property (B)
comparison theorem; advanced argument; property (B)
Summary:
In this paper we compare the asymptotic behaviour of the advanced functional equation \[ L_nu(t)-F\big (t,u[g(t)]\big )= 0\] with the asymptotic behaviour of the set of ordinary functional equations \[ \alpha _iu(t)-F\big (t,u(t)\big )= 0. \] On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.
References:
[1] Foster, K. E., Grimmer, R. C.: Nonoscillatory solutions of higher order differential equations. J. Math. Anal. Appl. 71 (1979), 1-17. MR 0545858
[2] Hille, E.: Non-oscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234-258. MR 0027925 | Zbl 0031.35402
[3] Kiguradze, I. T.: On the oscillation of solutions of the equation $d^mu/dt^m + a(t)|u|^n sign\,u = 0$. Mat. Sb. 65 (1964), 172-187. (Russian) MR 0173060 | Zbl 0135.14302
[4] Kusano, T., Naito, M.: Comparison theorems for functional differential equations with deviating arguments. J. Math. Soc. Japan 3 (1981), 509-532. MR 0620288
[5] Kusano, T., Naito, M., Tanaka, K.: Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations. Proc. Roy. Soc. Edinburg 90 (1981), 25-40. MR 0636062
[6] Trench, W. F.: Canonicals form and principal systems for general disconjugate equations. Trans. Amer. Math. Soc. 189 (1974), 319-327. MR 0330632
Search
Partner of
