Global solution curve and exact multiplicity of positive solutions for a class of fourth-order beam equations with clamped boundary conditions are derived. The results extend atheorem of P. Korman (2004) by allowing the presence of a singularity in the nonlinearity. The paper also establishes an a priori estimate for C^3-norm of positive solutions, which is optimal in Holder regularity. Applications to MEMS/NEMS models are presented.
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