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

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1. CMB 2011 (vol 56 pp. 659)

Yu, Zhi-Xian; Mei, Ming
Asymptotics and Uniqueness of Travelling Waves for Non-Monotone Delayed Systems on 2D Lattices
We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D lattice equations with non-monotone birth functions. First, with the help of Ikehara's Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier results in the literature.

Keywords:2D lattice systems, traveling waves, asymptotic behavior, uniqueness, nonmonotone nonlinearity
Category:35K57

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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