1. CMB 2011 (vol 56 pp. 378)
 Ma, Li; Wang, Jing

Sharp Threshold of the GrossPitaevskii Equation with Trapped Dipolar Quantum Gases
In this paper, we consider the GrossPitaevskii equation for the
trapped dipolar quantum gases. We obtain the sharp criterion for the
global existence and finite time blow up in the unstable regime by
constructing a variational problem and the socalled invariant
manifold of the evolution flow.
Keywords:GrossPitaevskii equation, sharp threshold, global existence, blow up Categories:35Q55, 35A05, 81Q99 

2. CMB 2011 (vol 55 pp. 285)
 Eloe, Paul W.; Henderson, Johnny; Khan, Rahmat Ali

Uniqueness Implies Existence and Uniqueness Conditions for a Class of $(k+j)$Point Boundary Value Problems for $n$th Order Differential Equations
For the $n$th order nonlinear differential equation, $y^{(n)} = f(x, y, y',
\dots, y^{(n1)})$, we consider uniqueness implies uniqueness and existence
results for solutions satisfying certain $(k+j)$point
boundary conditions for $1\le j \le n1$ and $1\leq k \leq nj$. We
define $(k;j)$point unique solvability in analogy to $k$point
disconjugacy and we show that $(nj_{0};j_{0})$point
unique solvability implies $(k;j)$point unique solvability for $1\le j \le
j_{0}$, and $1\leq k \leq nj$. This result is
analogous to
$n$point disconjugacy implies $k$point disconjugacy for $2\le k\le
n1$.
Keywords:boundary value problem, uniqueness, existence, unique solvability, nonlinear interpolation Categories:34B15, 34B10, 65D05 
