On a new approach for studying asymptotic behavior of solutions to singular differential equations

Abstract

Abstract. In the work we propose a new approach for studying the asymptotic behavior for large of the solutions to singular linear two-terms differential equationswith a potential ( ) growing non-regularly as → ∞. The idea of constructing the asymptotics for the solutions of singular linear differential equations and its effectiveness is demonstrated for 4 th order equations with an oscillating potential.