Asymptotics of Solutions of the Sturm–Liouville Equation with Respect to a Parameter - Gomilko, A. M.; Pivovarchik, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
On a finite segment [0, l], we consider the differential equation ( a( x )y′ ( x ) )′ + [ μ ρ _1 ( x ) + ρ _2 ( x ) ]y( x ) = 0 with a parameter μ ∈ C. In the case where a(x), ρ(x) ∈ L ∞[0, l], ρ j (x) ∈ L 1[0, l], j = 1, 2, a(x) ≥ m 0 > 0 and ρ(x) ≥ m 1 > 0 almost everywhere, and a(x)ρ(x) is a function absolutely continuous on the segment [0, l], we obtain exponential-type asymptotic formulas as \(| μ | → ∞\) for a fundamental system of solutions of this equation.