Geodesic
On asymptotics of solutions to some linear differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 103-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we find the principal asymptotic term at infinity of a certain fundamental system of solutions to the equation $l_{2n}[y]=\lambda y$ of order $2n$, where $l_{2n}$ is the product of second-order linear differential expressions and $\lambda$ is a fixed complex number. We assume that the coefficients of these differential expressions are not necessarily smooth but have a prescribed power growth at infinity. The asumptotic formulas obtained are applied for the problem on the defect index of differential operators in the case where $l_{2n}$ is a symmetric (formally self-adjoint) differential expression.
Keywords: principal asymptotic term, quasi-derivative, product of quasi-differential expressions, differential operator, defect index. 
@article{INTO_2017_141_a8,
     author = {K. A. Mirzoev and N. N. Konechnaja and T. A. Safonova and R. N. Tagirova},
     title = {On asymptotics of solutions to some linear differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {103--110},
     year = {2017},
     volume = {141},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_141_a8/}
}
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K. A. Mirzoev; N. N. Konechnaja; T. A. Safonova; R. N. Tagirova. On asymptotics of solutions to some linear differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Spectral theory, Tome 141 (2017), pp. 103-110. http://geodesic.mathdoc.fr/item/INTO_2017_141_a8/