Summary: Multiple Positive Solutions for a Three-Point Boundary
Department of Mathematics and Computer Science, Concordia College
Moorhead, Minnesota 56562
We will find conditions on f that lead to the existence of at least three positive solutions
to the three-point boundary value problem
-x (t) + f(x(t)) = 0, with x(0) = x (t2) = x (1) = 0
on [0, 1], where t2 1
2 , 1 . A positive solution will mean a solution in the cone of
nonnegative functions in the Banach space C[0, 1] with the sup norm.
Key words: ordinary differential equations, multipoint boundary value problem, Green's func-
tion, fixed point, cone.
AMS Subject Classification: 34B10.
A nonempty closed convex set P contained in a real Banach space E is called a cone if it
satisfies the following two conditions:
(i) if x P and 0 then x P;