On periodic solutions of the nonlinear suspension bridge equation (Q810313)

This paper is devoted to the study of the nonlinear oscillations of \[ - Ku_{xxtt}+u_{tt}+u_{xxxx}+bu^+=1+k \cos x+h(x,t), \] assuming that u and \(u_{xx}\) vanish for \(x=\pm \pi /2\), \(t>0\). The main results deal with the special cases \(K=1/4\), \(b\in (4,19)\) and \(K=0\), \(b=b(x)\). Existence, uniqueness, and nonuniqueness theorems are given. The treatment is very elegant. Moreover, there seem to be a number of natural, open questions associated with this equation.