On the minimal problem in the theory of differential equations of oscillations of an elastic inhomogeneous rod

Abstract

The question of the existence of so-called 'fundamental functions' for higher-order differential equations has been the subject of research in a number of works, but undoubtedly further elaboration is possible in the sense of applying various methods to its solution. This article represents an attempt to generalize the method of the American geometer Max Mason, as expounded by him for second-order differential equations, to the case of fourth-order differential equations, to which, as is known, the question of the oscillations of an elastic inhomogeneous rod reduces.

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