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

被引：22

作者：

Shkalikov, A. A. ^{[1
]}

Vladykina, V. E. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2015年 / 98卷 / 5-6期

基金：

俄罗斯科学基金会;

关键词：

Sturm-Liouville equation; asymptotic solution; singular coefficient; Volterra integral operator; fundamental system of solutions; LINEAR-DIFFERENTIAL EQUATIONS; POTENTIALS; OPERATORS;

D O I：

10.1134/S0001434615110218

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain asymptotic representations as lambda ->infinity 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, x is an element of [a, b] subset of 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].

引用

页码：891 / 899

页数：9

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