LAUSR

AbstractAsymptotic formulas as x→∞ are obtained for a fundamental system of solutions to equations of the form $$l\left( y \right): = {\left( { - 1} \right)^n}{\left( {p\left( x \right){y^{\left( n \right)}}} \right)^{\left( n \right)}} + q\left( x \right)y = \lambda y,x \in [1,\infty )$$l(y):=(−1)n(p(x)y(n))(n)+q(x)y=λy,x∈[1,∞), where p is a locally integrable function representable as $$p\left( x \right) = {\left( {1 + r\left( x \right)} \right)^{ - 1}},r \in {L^1}\left( {1,\infty } \right)$$p(x)=(1+r(x))−1,r∈L1(1,∞), 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 $$\sigma \in {L^1}\left( {1,\infty } \right)ifk < n,$$σ∈L1(1,∞)ifk