The Distribution of Zeros of the Solutions of Linear Homogeneous Differential Equations of the Sixth Order Using Semi-critical Intervals

Main Article Content

Kathim A. H
Wafaa M. Taha

Abstract

In this pap, we investigate the distribution of zeros for the solution of linear Homogeneous Differential Equations (LHDE) in the semi-critical intervals ,for the boundary value problems. The method used in this paper is different from [1-3] in which the authors used geometric approach to distribute the zeros of the solutions of LHDE. We used an analytic approach. Moreover we stated the relation between semi-critical intervals for the boundary value problems .

Article Details

How to Cite
Kathim A. H, & Wafaa M. Taha. (2023). The Distribution of Zeros of the Solutions of Linear Homogeneous Differential Equations of the Sixth Order Using Semi-critical Intervals. Tikrit Journal of Pure Science, 21(3), 162–165. https://doi.org/10.25130/tjps.v21i3.1010
Section
Articles

References

[1]- Alive R. G., 1962, On the question of distribution of zeros of solutions of linear differential equations of fourth order, Recnts. of Sci. Asp. Conf., Kazan Ins . .

[2]- Peterson A. C., 1969, Distribution of Zeros Solution of Fourth Order Differential Equation, Pacific Journal of mathematics, Vol.30, P 751-764.

[3]-Jerry R. Ridenhouk, 1974, On the Zeros of Solutions of Nth Order Linear Differential Equations , Journal of Differential Equations 16, p 45-71.

[4]- Al-Jawfi S.A., Kathim A.H., 2012.The laws of the distribution of zeros of solutions of a linear differential equation of order 5. Herald of Dagestan state university ( DSU). Vol. 1,p. 79–86.

[5]- Al-Jawfi S.A.,2012, Limit relations between the semi-critical intervals solutions of multipoint boundary value problems for linear fifth-order differential equation. Herald of Dagestan state university ( DSU). Vol. 6, p. 61–66.

[6]- Al-Jawfi S.A., 2012, On the disappearance non-trivial solutions of multipoint boundary value problems in the non-trivial in the case of a linear differential equation of fifth order, Herald of Dagestan state university (DSU). Vol. 6,p. 119–126.

[7]- Al-Jawfi S.A.,2012, On nontrivial solutions of the homogeneous multi-point boundary value problems for linear fifth-order differential equation, Herald of Dagestan state university ( DSU). Vol. 6, p. 87–92.

[8]- Al-Jawfi S.A., MD Jasim, Kathim A.H., 2012, The laws of the distribution of zeros of solutions boundary value problem Vallée Poussin of linear differential equation of the fifth-order // Modern methods of boundary value problems(Spring materials Voronezh Mathematical School "Pontryagin reading - XXI»). Voronezh., p. 6-9.

[9]- Al-Jawfi S.A., Kathim A.H., 2012, The laws of the distribution of zeros of solutions of a linear differential equation of order 5// Collection of scientific articles on materials of the IV-th International scientific-practical conference, Stavropol, Samara State Aerospace University September 28-29, p. 103-109.

[10]- G. Sansone, 1953, Ordinary Differential Equations, Part 1, Moscow, (in Russian).

[11]- Shan Wenrui, Niu Zhilei, Guo Yanping, 2007, The distribution of zeros of solutions for a class of neutral delay differential equations, Science Direct Applied Mathematics and Computation 186 (2007), p 1137–1150.