This article is cited in 23 papers

Asymptotics of the Solutions of the Sturm–Liouville Equation with Singular Coefficients

V. E. Vladikina, A. A. Shkalikov

Lomonosov Moscow State University

Abstract: We obtain asymptotic representations as $\lambda \to \infty$ in the upper and lower half-planes for the solutions of the Sturm–Liouville equation
$$ -y''+p(x)y'+q(x)y= \lambda ^2 \rho(x)y, \qquad x\in [a,b] \subset \mathbb{R}, $$
under the condition that $q$ is a distribution of first-order singularity, $\rho$ is a positive absolutely continuous function, and $p$ belongs to the space $L_2[a,b]$.

Keywords: Sturm–Liouville equation, asymptotic solution, singular coefficient, Volterra integral operator, fundamental system of solutions, space of bounded functions.

UDC: 517.928+517.984

Received: 06.10.2015

DOI: 10.4213/mzm10976

 English version: Mathematical Notes, 2015, 98:6, 891–899

Bibliographic databases:

• 
• 
• 
•