Abstract
Asymptotic formulas as x→∞ are obtained for a fundamental system of solutions to equations of the form
, where p is a locally integrable function representable as
, and q is a distribution such that q = σ(k) for a fixed integer k, 0 ≤ k ≤ n, and a function σ satisfying the conditions \(\sigma \in {L^1}\left( {1,\infty } \right)ifk < n,\)\(\left| \sigma \right|\left( {1 + \left| r \right|} \right)\left( {1 + \left| \sigma \right|} \right) \in {L^1}\left( {1,\infty } \right)ifk = n\) . Similar results are obtained for functions representable as
, for fixed k, 0 ≤ k ≤ n, where the functions r and s satisfy certain integral decay conditions. Theorems on the deficiency index of the minimal symmetric operator generated by the differential expression l(y) (for real functions p and q) and theorems on the spectra of the corresponding self-adjoint extensions are also obtained. Complete proofs are given only for the case n = 1.
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Original Russian Text © N.N. Konechnaya, K.A. Mirzoev, A.A. Shkalikov, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 2, pp. 231–242.
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Konechnaya, N.N., Mirzoev, K.A. & Shkalikov, A.A. On the Asymptotic Behavior of Solutions to Two-Term Differential Equations with Singular Coefficients. Math Notes 104, 244–252 (2018). https://doi.org/10.1134/S0001434618070258
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DOI: https://doi.org/10.1134/S0001434618070258