 
Summary: ROCKY MOUNTAIN
JOURNAL OF MATHEMATICS
Volume 36, Number 2, 2006
A FOURTHORDER FOURPOINT
RIGHT FOCAL BOUNDARY VALUE PROBLEM
DOUGLAS R. ANDERSON AND RICHARD I. AVERY
ABSTRACT. We are concerned with the unit interval right
focal boundary value problem x(4)(t) = f(x(t)), x(0) =
x (q) = x (r) = x (1) = 0. Under various assumptions on f
and the real numbers 0 < q < r < 1 we prove the existence of
positive solutions for this boundary value problem by applying
a generalization of the LeggettWilliams fixed point theorem,
the Five Functionals FixedPoint Theorem.
1. Introduction. The literature on positive solutions to boundary
value problems is extensive. The recent book by Agarwal, Wong and
O'Regan [2] gives a good overview for much of the work which has
been done and the methods used. More specifically the monograph
by Agarwal [1] gives a thorough discussion of previously known results
related to right focal boundary value problems. Anderson [3] extended
these known results by finding and giving conditions for the positivity of
