ANALOGUE OF STURM’S THEOREM FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH MEASURE DERIVATIVES
The paper proves analog of Sturm’s theorem for fourth-order differential equations with nonsmooth solutions, which are important in the analysis of the qualitative properties of solutions. In the analysis of solutions to the equation, we use the pointwise approach proposed by Yu. V. Pokorny and which has shown its effectiveness in studying equations not only of the second order, but also of a higher order, in particular, an exact parallel is constructed to the classical theory of qualitative theory up to oscillation theorems.