In this paper, we consider the existence of extremal solutions for nonlinear fourth-order differential equation. By use a new comparison result, some sufficient conditions are established by combining monotone iterative technique and methods lower upper solutions. Finally, an example is given to illustrate validity our main results.

Atomic force microscopy (AFM)-based single-molecule force spectroscopy (SMFS) enables a wide array of studies, from measuring the strength of a ligand-receptor bond to elucidating the complex folding pathway of individual membrane proteins. Such SMFS studies and, more generally, the diverse applications of AFM across biophysics and nanotechnology are improved by enhancing data quality via impro...

Optical beam deflection systems are widely used in cantilever based atomic force microscopy (AFM). Most commercial cantilevers have a reflective metal coating on the detector side to increase the reflectivity in order to achieve a high signal on the photodiode. Although the reflective coating is usually much thinner than the cantilever, it can still significantly contribute to the damping of th...

In this paper, the capabilities of displacement curvature derived from static response data for finding the location and severity of damage in Euler-Bernoulli beams are assessed. Static response of a beam is obtained using the finite element modeling. In order to reduce the number of measured nodal displacements, the beam deflection is fitted through a polynomial function using a limited number...

We report a direct measurement of the friction coefficient of a fluctuating (and slipping) contact line using a thin vertical glass fiber of diameter d with one end glued onto a cantilever beam and the other end touching a liquid-air interface. By measuring the broadening of the resonant peak of the cantilever system with varying liquid viscosity η, we find the friction coefficient of the conta...

Microcantilever-based sensors can be used to detect molecular absorption of, for example, hydrogen gas, which causes changes in the surface stress, leading to deflection of the cantilever. Such a deflection can be determined by means of optical beam deflection, capacitance-, or piezo-resistance based readout. We have recently proposed a compact integrated mechano-optical sensor using a novel an...