Refined blow-up results for nonlinear fourth order differential equations (Q2339850)

The nonlinear fourth order differential equation \[ w''''(x) - Tw''(x) + f(w(x)) = 0, \quad x \in {\mathbb R}, \] which arise as models of suspension of bridges, is considered, where \(T \in {\mathbb R}\) and \(f\) is a locally Lipschitz function. It is known that solutions may blow up in finite time, if the initial data satisfy some positivity assumption and \(f\) is a power-like nonlinearity function. In this paper, the authors extend it to more general nonlinearities allowing exponential growth and to a wider class of initial data. Some hints on how to prevent blow-up are also given.