Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Philip Kormana1

a1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA

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.

(Received July 10 2003)

(Accepted November 19 2003)