Geodesic
On a~new approach for studying asymptotic behavior of solutions to singular differential equations
Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 9-14

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In the work we propose a new approach for studying the asymptotic behavior for large $x$ of the solutions to singular linear two-terms differential equations $$ -\frac{d^n}{dx^n}y(x,\lambda)+\lambda q(x)y(x,\lambda)=0 $$ with a potential $q(x)$ non-regular growing as $x\to\infty$. The idea of constructing the asymptotics for the solutions of singular linear differential equations and its effectiveness is demonstrated for 4th order equations with an oscillating potential.
Keywords: spectral theory of differential operators, asymptotic formulae for solutions to differential equations. 
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     title = {On a~new approach for studying asymptotic behavior of solutions to singular differential equations},
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N. F. Valeev; E. A. Nazirova; Ya. T. Sultanaev. On a~new approach for studying asymptotic behavior of solutions to singular differential equations. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 9-14. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a1/