On the stability of periodic solutions with defined sign in MEMS via lower and upper solutions

Periodic Oscillations in MEMS under Squeeze Film Damping Force

“…where V 2 = 1/T Ð T 0 V 2 ðtÞdt: Additionally, respect to the results over the Nathanson model with constant damping given in [7,9], the criteria that we illustrated over the function ∂ x gðt, xÞ − c 2 /4 in Theorem 5 have the advantage that considers the L p norms ðp ∈ ½1,∞Þ, and not over the supremum of its range. In consequence, Theorem 5 leads to a refinement of the results founded in [7,9].…”

“…In this section, we consider the Duffing equation: x, c ≥ 0, and c ∈ R. The existence and stability of periodic solutions of (50) have been considered in [9] for the case c = 0 and also in [7] for c > 0. The results exposed here respect to (50) have the purpose to combine the ideas found in the mentioned papers and the results of Theorems 15 and 16 in the Appendix.…”

“…After more than 50 years, the Nathanson model continues to draw a lot of attention. Many researchers have been devoted to its analytical and numerical study, mainly to understanding and characterizing the pull-in phenomenon through different techniques and mathematical formulations (see for instance [1,2,[6][7][8][9][10]).…”

“…When the damping force FD is given by (2) (namely, the linear damping force), the authors in [7,9] present a rigorous analysis of the existence and stability of exactly two positive T-periodic solutions of ( 6) for the nonconservative (c ≠ 0) and for the conservative case (c = 0), respectively. In both papers, classical functional and topological techniques were employed such as the upper and lower solution method, Leray-Schauder degree, and the topological index of a periodic solution.…”

Periodic oscillations for a graphene-based electrostatic micro actuator

“…In [16] the authors consider the Nathanson's model and the Comb-drive finger model with cubic stiffness and without damping, and obtain existence, multiplicity and linear stability results for positive periodic solutions. A new stability phenomenon is underlying in the Comb-drive model for large cubic stiffness.…”