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Search: MSC category 34B24 ( Sturm-Liouville theory [See also 34Lxx] )

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1. CMB 2011 (vol 56 pp. 102)

Kong, Qingkai; Wang, Min
Eigenvalue Approach to Even Order System Periodic Boundary Value Problems
We study an even order system boundary value problem with periodic boundary conditions. By establishing the existence of a positive eigenvalue of an associated linear system Sturm-Liouville problem, we obtain new conditions for the boundary value problem to have a positive solution. Our major tools are the Krein-Rutman theorem for linear spectra and the fixed point index theory for compact operators.

Keywords:Green's function, high order system boundary value problems, positive solutions, Sturm-Liouville problem
Categories:34B18, 34B24

2. CMB 1998 (vol 41 pp. 23)

Clemence, Dominic P.
Subordinacy analysis and absolutely continuous spectra for Sturm-Liouville equations with two singular endpoints
The Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.

Categories:34L05, 34B20, 34B24

3. CMB 1997 (vol 40 pp. 416)

Clemence, Dominic P.
On the singular behaviour of the Titchmarsh-Weyl $m$-function for the perturbed Hill's equation on the line
For the perturbed Hill's equation on the line, $$ -\frac{d^2y}{dx^2}+ [P (x) +V (x )] y=Ey,\quad -\infty
Categories:34L05, 34B20, 34B24

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