On a Method for Studying the Asymptotics of Solutions of Sturm–Liouville Differential Equations with Rapidly Oscillating Coefficients

On the Asymptotic of Solutions of Odd Order Two-Term Differential Equations

“…Such bifurcation points for differential equations and (systems of equations) with regularly oscillating coefficients are typical and were recently noted by us in works devoted to the study of the asymptotic behavior of the Sturm-Liouville equation with an oscillating potential ( [4,14]).…”

“…The use of this approach made it possible to obtain new asymptotic formulas in different cases. For example, in [4,12,14] new asymptotic formulas were obtained for solutions of the Sturm-Liouville equation…”

“…Here we develop an approach that was proposed in [4,[8][9][10][11][12][13][14] and can be implemented to study the asymptotic behavior as x → ∞ of a fundamental system of solutions of two-term equation of arbitrary odd order of the form…”

“…Therefore, the study of the asymptotic behavior of solutions to equations with coefficients from other classes of functions is of particular interest. Such classes of functions were described by us in the papers [4]. Let us also note the works [5][6][7], where differential operators with distribution coefficients were studied.…”

“…Since 2014 we have published a series of articles devoted to the study of the asymptotic behavior of solutions to singular ODEs with regularly oscillating coefficients ( [4,[8][9][10][11][12][13][14]). In this case, a new approach was used for the study, based on a sequence of matrix transformations and the use of Campbell's identity [16].…”