REGULARIZATION OF TWO-TERM DIFFERENTIAL EQUATIONS WITH SINGULAR COEFFICIENTS BY QUASIDERIVATIVES

被引：16

作者：

Goryunov, A. S. ^{[1
]}

Mikhailets, V. A. ^{[1
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2012年 / 63卷 / 09期

关键词：

Hilbert Space; Operator Function; Symmetric Operator; Minimal Operator; Homogeneous Boundary Condition;

D O I：

10.1007/s11253-012-0584-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a regularization of the formal differential expression l(y) = i(m) y((m))(t) + q(t)y(t), t is an element of (a, b), of order m >= 3 by quasiderivatives. It is assumed that the distribution coefficient q has the antiderivative Q is an element of L ([a, b]; C). In the symmetric case. (Q = (Q) over bar), we describe self-adjoint and maximal dissipative/accumulative extensions of the minimal operator and its generalized resolvents. In the general (nonself-adjoint) case, we establish the conditions of convergence for the resolvents of the analyzed operators in norm. The case where m = 2 and Q is an element of L-2 ([a, b]; C) was studied earlier.

引用

页码：1361 / 1378

页数：18