1. CMB 2012 (vol 56 pp. 466)
|Inclusion Relations for New Function Spaces on Riemann Surfaces|
We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, BMOA or the recently defined $Q_p$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces.
Keywords:Bloch space, BMOA, $Q_p$, Green's function, hyperbolic Riemann surface
Categories:30F35, 30H25, 30H30
2. CMB 2011 (vol 56 pp. 102)
|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