Global bifurcation curves for fourth-order MEMS/NEMS models II

TL;DR

This paper extends the analysis of fourth-order beam equations with singular nonlinearities, deriving global solution curves and multiplicity results, with applications to MEMS/NEMS devices.

Contribution

It generalizes Korman's theorem by including singularities and establishes optimal a priori estimates for positive solutions.

Findings

Derived global bifurcation curves for fourth-order equations.

Proved multiplicity of positive solutions under singular nonlinearities.

Applied results to MEMS/NEMS models.

Abstract

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.