IJPAM: Volume 56, No. 2 (2009)

CHARACTERIZATION OF PARTIAL DERIVATIVES WITH
RESPECT TO BOUNDARY CONDITIONS FOR NONLOCAL
BOUNDARY VALUE PROBLEMS FOR $N$-TH ORDER
DIFFERENTIAL EQUATIONS

Johnny Henderson$^1$, Jeffrey W. Lyons$^2$
$^{1,2}$Department of Mathematics, Campus Box 97328
Baylor University
Waco, Texas, 76798-7328, USA
$^1$e-mail: Johnny_Henderson@baylor.edu
$^2$e-mail: Jeff_Lyons@baylor.edu


Abstract.Under certain conditions, solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y'$, $\ldots, y^{(n-1)})$, $y(x_i) = y_i$ for $1\leq i\leq n-1$, and $y(x_n) - \sum_{k=1}^m r_i y(\eta_i) = y_n$, are differentiated with respect to boundary conditions, where $a < x_1 < x_2< \cdots < x_{n-1} < \eta_1 < \cdots < \eta_m < x_n < b$, $r_1, \ldots, r_m, y_1, \ldots, y_n \in \R$.

Received: August 31, 2009

AMS Subject Classification: 34B10, 34B15

Key Words and Phrases: nonlinear boundary value problem, ordinary differential equation, nonlocal boundary condition, existence, uniqueness

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 2