 
Summary: Corollary to the Five Functionals Fixed Point Theorem
Douglas R. Anderson
Department of Mathematics and Computer Science, Concordia College
Moorhead, MN 56562
andersod@cord.edu
Richard I. Avery
College of Natural Sciences, Dakota State University
Madison, SD 57042
averyr@pluto.dsu.edu
Johnny Henderson
Department of Mathematics, Auburn University
Auburn, Alabama 368495310
hendej2@mail.auburn.edu
Abstract
Conditions for the functionals contained in the Five Functionals Fixed Point Theorem are
determined to guarantee the existence of at least two positive xed points for a nonlinear
operator. For the second order boundary value problem, y
HH + f (y) = 0, 0 t 1,
y(0) = 0 = y(1), where f : R ! [0; 1); growth conditions are imposed on f which yield
the existence of at least two positive solutions. We then make a comparison to the growth
