Asymptotics of the system of solutions of a general differential equation with parameter - Rykhlov, V. S. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We consider annth-order differential equation a_0 (x)y^(n) (x) + a_1 (x)y^(n - 1) (x) + ... + a_n (x)y(x) = λ y(x) with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that \(j = 1,n \) anda 0 (x) is an absolutely continuous function which does not turn into zero on the interval [a, b], we establish asymptotic formulas of exponential type for the fundamental system of solutions of this equation provided that |λ| is sufficiently large.