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IMA Journal of Applied Mathematics 1999 63(1):37-49; doi:10.1093/imamat/63.1.37
© 1999 by Institute of Mathematics and its Applications
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Multiple periodic solutions for a nonlinear suspension bridge equation

LD Humphreys and PJ McKennaA1

Rhode Island College, Providence, Rhode Island 02908, USA A1 University of Connecticut, Storrs, CT 060268, USA

We investigate nonlinear oscillations in a fourth-order partial differential equation which models a suspension bridge. Previous work establishes multiple periodic solutions when a parameter exceeds a certain eigenvalue. In this paper, we use Leray-Schauder degree theory to prove that if the parameter is increased further, beyond a second eigenvalue, then additional solutions are created.


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