Asymptotics of the system of solutions of a general differential equation with parameter

  • V. S. Rykhlov

Abstract

We consider annth-order differential equation $$a_0 (x)y^{(n)} (x) + a_1 (x)y^{(n - 1)} (x) + ... + a_n (x)y(x) = \lambda y(x)$$ with parameter λ ∈ ℂ on a finite interval [a,b]. Under the conditions that \(j = \overline {1,n} \) 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.
Published
25.01.1996
How to Cite
RykhlovV. S. “Asymptotics of the System of Solutions of a General Differential Equation With Parameter”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 1, Jan. 1996, pp. 96-108, https://umj.imath.kiev.ua/index.php/umj/article/view/5367.
Section
Research articles