一般形式 Sturm-Liouville 方程的奇异 Dirichlet 边界问题可解性的必要条件和充分条件

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-11-04 DOI:10.1016/j.jde.2024.10.023

N. Chernyavskaya , L. Shuster

引用次数: 0

摘要

我们考虑以下条件下的边界问题(1)-(r(x)y′(x))′+q(x)y(x)=f(x),x∈R,(2)lim|x|→∞y(x)=0：1)r>0,1r∈L1loc(R),q∈L1loc(R);2)equation (1) is correctly solvable in Lp(R), p∈(1,∞).我们得到了函数 r 和 q 的必要条件和充分条件，在这些条件下，无论选择哪个函数 f∈Lp(R),p∈(1,∞)，方程 (1) 的解 y∈Lp(R) 都满足 (2)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Necessary and sufficient conditions for the solvability of a singular Dirichlet boundary problem for the Sturm-Liouville equation of general form

We consider the boundary problem(1)

- {(r (x) y^{'} (x))}^{'} + q (x) y (x) = f (x), x \in R,

(2)

\lim_{| x | \to \infty} y (x) = 0

under the following conditions:

1)
$r > 0, \frac{1}{r} \in L_{1}^{loc} (R), q \in L_{1}^{loc} (R)$ ;
2)
equation (1) is correctly solvable in $L_{p} (R)$ , $p \in (1, \infty)$ .

We obtain necessary and sufficient requirements for the functions r and q under which, regardless of the choice of a function

f \in L_{p} (R)

p \in (1, \infty)

, the solution

y \in L_{p} (R)

of equation (1) satisfies (2).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics