Distribution of zeros of solutions of sixth order (2 ≤ n ≤ 5)-points boundary value problem in terms of semi-critical intervals

Document Type : Research Paper


1 Department of Mathematics, University of Ibb, Ibb, Yemen.

2 Mathematics, College of Science, University of Sulaimani, Sulaimani, Iraq


In this paper, the issue of distribution of zeros of the solutions of linear homogenous differential equations (LHDE) have been investigated in terms of semi-critical intervals. We shall follow a geometric approach to state and prove some properties of LHDEs of the sixth order with (2, 3, 4, and 5 points) boundary conditions and with measurable coefficients. Moreover, the relations between semi-critical intervals of the LHDEs have been explored. Also, the obtained results have been generalized for the 5th order differential equations.