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].
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页码：891 / 899
页数：9
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