Summary: Journal of Mathematical Analysis and Applications
288:1 (2003) 1­14.
GREEN'S FUNCTION FOR A THIRD-ORDER GENERALIZED
RIGHT FOCAL PROBLEM
DOUGLAS R. ANDERSON
Abstract. We determine the Green's function for the third-order three-
point generalized right focal boundary value problem
x (t) = 0 t1 t t3
x(t1) = x (t2) = 0
x(t3) + x (t3) = 0,
> 0, and determine conditions on the coefficients and boundary points
to ensure its positivity. Then we use the Krasnoselskii and Leggett and
Williams fixed point theorems to prove the existence of solutions to the
nonlinear problem
x (t) = f(t, x(t)) t1 t t3
x(t1) = x (t2) = 0
x(t3) + x (t3) = 0,
for certain constraints placed on nonnegative f.
1. finding green's function
We are concerned with the third-order three-point generalized right focal

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

Collections: Mathematics