Article
Ufa Mathematical Journal
Volume 7, Number 3, pp. 9-14
On a new approach for studying asymptotic behavior of solutions to singular differential equations
Nazirova E.A., Sultanaev Y.T., Valeev N.F.
DOI:10.13108/2015-7-3-9
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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 $q(x)$ growing non-regularly as $x\rightarrow \infty$. The idea of constructing the asymptotics for the solutions of singular linear differential equations and its effectiveness is demonstrated for $4^{\mathrm{th}}$ order equations with an oscillating potential.