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J. Math. Anal. Appl. 323 (2006) 958973 www.elsevier.com/locate/jmaa

Summary: J. Math. Anal. Appl. 323 (2006) 958973
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
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