Abstract
This paper addresses the issue of the relations between semi-critical intervals of LHDE of the seventh order with (2, 3, 4, and 5 points) boundary conditions and with measurable coefficients. We shall use the geometric approach to state and prove some properties of LHDE. Moreover, the distribution of zeros in the solutions of the linear homogeneous differential equations (LHDE) has also been explored. The obtained results have been generalized for the sixth-order differential equation.
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