Asymptotic Expansions of Second Order Linear Differential Equations Having Conditionally Integrable Coefficients
Ronald I. Becker · Journal of the London Mathematical Society · 1979
Asymptotic expansions of (px′)′+(f+g)x = 0 where the solutions φ and ψ of (px′)′+fx = 0 are bounded and ∫ t ∞ g φ 2 and ∫ t ∞ g ϕ 2 are conditionally integrable are obtained. These are used to generalize results of Atkinson [4] and Harris and Lutz [5] on the asymptotic expansions of x″+(1+g)x = 0. The results are applied to the limit-circle classification of second-order linear differential operators.