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ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
 

Summary: ROCKY MOUNTAIN
JOURNAL OF MATHEMATICS
Volume 36, Number 2, 2006
A FOURTH-ORDER FOUR-POINT
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 Leggett-Williams fixed point theorem,
the Five Functionals Fixed-Point 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

  

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

 

Collections: Mathematics