Distribution of zeros of solutions of sixth order (۲ ≤ n ≤ ۵)-points boundary value problem in terms of semi-critical intervals

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 (۲, ۳, ۴, and ۵ 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 ۵th order differential equations.

Keywords:

Linear differential equations , Distribution of zeros for the solution , Boundary value problems , Semi-oscillatory interval , Semi-critical interval