Multiplicity results for nonlinear wave equations with nonlinearities crossing eigenvalues (Q1895936)

The existence of a solution for a nonlinear perturbation of the one- dimensional wave operator is established under Dirichlet conditions on the interval \(-\pi/2< x< \pi/2\) with \(\pi\)-periodic conditions with respect to \(t\). The problem is related to the behaviour of a string of non-uniform density vibrating in the vertical plane when the upward and downward acting forces are not uniform.