A representation for solutions of the Sturm-Liouville equation

被引：61
|
作者：
Kravchenko, Vladislav V. [1 ]
机构：
[1] IPN, CINVESTAV, Dept Math, Unidad Queretaro, Queretaro, Mexico
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2008年 / 53卷 / 08期
关键词：
Sturm-Liouville problem; pseudoanalytic functions; Vekua equation; Schrodinger equation; Darboux transformation;
D O I：
10.1080/17476930802102894
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A representation for the general solution of the equation (pu')' + qu = omega(2)u in terms of a non-trivial solution of (pu'(0))' + qu(0) = 0 is given. This result is obtained with the aid of the theory of pseudoanalytic functions and their relationship to solutions of the stationary two-dimensional Schrodinger equation. The representation has a simple and easily verifiable form and lends itself to numerical computation. Its applications to spectral problems are discussed.
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页码：775 / 789
页数：15
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