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Search: All articles in the CMB digital archive with keyword existence

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1. CMB 2011 (vol 56 pp. 378)

Ma, Li; Wang, Jing
Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases
In this paper, we consider the Gross-Pitaevskii 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 so-called invariant manifold of the evolution flow.

Keywords:Gross-Pitaevskii 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, $y^{(n)} = f(x, y, y', \dots, y^{(n-1)})$, we consider uniqueness implies uniqueness and existence results for solutions satisfying certain $(k+j)$-point boundary conditions for $1\le j \le n-1$ and $1\leq k \leq n-j$. We define $(k;j)$-point unique solvability in analogy to $k$-point disconjugacy and we show that $(n-j_{0};j_{0})$-point unique solvability implies $(k;j)$-point unique solvability for $1\le j \le j_{0}$, and $1\leq k \leq n-j$. This result is analogous to $n$-point disconjugacy implies $k$-point disconjugacy for $2\le k\le n-1$.

Keywords:boundary value problem, uniqueness, existence, unique solvability, nonlinear interpolation
Categories:34B15, 34B10, 65D05

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