Summary: J. Math. Anal. Appl. 323 (2006) 958­973
www.elsevier.com/locate/jmaa
Existence of solutions for a cantilever beam problem
Douglas R. Anderson a,
, Joan Hoffacker b
a Department of Mathematics, Concordia College, Moorhead, MN 56562, USA
b Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA
Received 1 November 2005
Available online 2 December 2005
Submitted by William F. Ames
Abstract
We are concerned with the fourth-order nonuniform cantilever beam problem
I(x)W (x)

= f x,W(x) ,
W(a) = W (a) = 0, I(b)W (b) = (I(x)W (x)) |x=b = 0. Under various assumptions on f we
prove the existence of at least one, two, or three positive solutions for this measure chain boundary value
problem using the Green function approach.
© 2005 Elsevier Inc. All rights reserved.
Keywords: Measure chains; Boundary value problems; Green function; Fixed points

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

Collections: Mathematics