Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1237.34143
El-Raheem, Zaki F.A.; Nasser, A.H.
The eigenfunction expansion for a Dirichlet problem with explosive factor. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 828176, 16 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

The authors consider the following Dirichlet eigenvalue problem for the Sturm-Liouville operator with explosive factor: $$-y^{\prime \prime} + q(x)y = \lambda \rho(x) y, ~0 \leq x \leq \pi, ~y(0) = y(\pi) = 0,$$ where $q(x) \geq 0$ has a second piecewise integrable derivative on $[0, \pi]$, $\rho(x)$ is the explosive factor defined as $\rho(x) = 1$ on $[0, a)$ with $a < \pi$, $\rho(x) = -1$ on $(a, \pi]$. By menas of the method of Green's function, they prove that the eigenfunction expansion formula is true both pointwise and in the $L^2$ norm.
[Chie-Ping Chu (Taipei)]

MSC 2000:: *34L10 Eigenfunction expansions, etc. (ODE)
34B24 Sturm-Liouville theory

Keywords: eigenfunction expansion; Dirichlet problem with explosive factor

Citations: Zbl 1034.34098

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]