Search results
Search: MSC category 34B10
( Nonlocal and multipoint boundary value problems )
1. 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 
