Global bifurcation curve for fourth-order MEMS/NEMS models. (Q2148410)

The authors investigate a MEMS/NEMS model described by the equations for a simply supported Euler-Bernoulli beam \[ u''''(x)=\mu g(u(x)), \] where \(\mu >0\) is a positive parameter and \(g(u)\) is a monotonically increasing function, which is allowed to possess a singularity, as it is common in MEMS models. Using results from the article [\textit{P. Korman}, Math. Methods Appl. Sci. 25, No. 1, 3--20 (2002; Zbl 1011.35046)] the authors prove, that there exists a critical parameter value \(\mu_0\), such that there exist two equilibria for \(\mu <\mu_0\), one equilibrium for \(\mu =\mu_0\) and no equilibria for \(\mu >\mu_0\).