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1. CMB 2011 (vol 56 pp. 102)
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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)
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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)
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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 |