On the possibility of the Fourier method using for finding of a solution of the sixth-order mathematical model with derivatives with respect to measure

Abstract

Abstract In the present paper the separation variables method is applied to finding an exact solution of the sixth-order mathematical model with nonsmooth solutions. Analyzing arising difficulties, in particular the spectral problem, we use a pointwise method of interpretation of solutions proposed by Yu.V. Pokornyi. This method showed its effectiveness in constructing of an exact parallel to the classical theory of differential equations, including oscillation theorems, both second and fourth orders.