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Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems

Published online by Cambridge University Press:  12 July 2007

Philip Korman
Philip Korman
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
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Abstract

Using techniques of bifurcation theory, we give exact multiplicity and uniqueness results for the fourth-order Dirichlet problem, which describes deflection of an elastic beam, subjected to a nonlinear force, and clamped at the end points. The crucial part of this approach was to show positivity of non-trivial solutions of the corresponding linearized problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 179 - 190
Copyright
Copyright © Royal Society of Edinburgh 2004

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